SAS Textbook Examples
Regression with Graphics by Lawrence Hamilton
Chapter 4: Regression Criticism
Correlation and Scatterplot Matrices
We will be using the concord1 data set. First, we need to change the variable retire
from a string to a numeric variable.
data concy;
set concord1;
retired = .;
if retire = 'yes' then retired = 1;
if retire = 'no' then retired = 0;
run;
page 114 Table 4.2 Correlation matrix for 1981 household water use and predictors.
proc corr data = concy;
var income water80 educat retired peop81 cpeop water81;
with income water80 educat retired peop81 cpeop water81;
run;
The CORR Procedure
7 With Variables: income water80 educat retired peop81 cpeop water81
7 Variables: income water80 educat retired peop81 cpeop water81
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
income 496 23.07661 13.05784 11446 2.00000 100.00000
water80 496 2732 1764 1355100 200.00000 12700
educat 496 14.00403 3.09055 6946 6.00000 20.00000
retired 496 0.29435 0.45621 146.00000 0 1.00000
peop81 496 3.07258 1.65718 1524 1.00000 10.00000
cpeop 496 -0.03831 0.48466 -19.00000 -3.00000 3.00000
water81 496 2298 1486 1140000 100.00000 10100
Pearson Correlation Coefficients, N = 496
Prob > |r| under H0: Rho=0
income water80 educat retired peop81 cpeop water81
income 1.00000 0.33705 0.34625 -0.38056 0.31128 0.09112 0.41779
<.0001 <.0001 <.0001 <.0001 0.0425 <.0001
water80 0.33705 1.00000 0.09822 -0.29193 0.52510 -0.03117 0.76479
<.0001 0.0287 <.0001 <.0001 0.4885 <.0001
educat 0.34625 0.09822 1.00000 -0.17421 0.05872 0.00550 0.04038
<.0001 0.0287 <.0001 0.1917 0.9028 0.3695
retired -0.38056 -0.29193 -0.17421 1.00000 -0.37569 -0.05854 -0.27313
<.0001 <.0001 <.0001 <.0001 0.1930 <.0001
peop81 0.31128 0.52510 0.05872 -0.37569 1.00000 0.14433 0.61831
<.0001 <.0001 0.1917 <.0001 0.0013 <.0001
cpeop 0.09112 -0.03117 0.00550 -0.05854 0.14433 1.00000 0.06611
0.0425 0.4885 0.9028 0.1930 0.0013 0.1415
water81 0.41779 0.76479 0.04038 -0.27313 0.61831 0.06611 1.00000
<.0001 <.0001 0.3695 <.0001 <.0001 0.1415
page 115 Figure 4.1 Scatterplot matrix corresponding to Table 4.2
(household water use and predictors). The %include command tells SAS the a macro will be
used. The macro is called scatter, so the %scatter is the command to use that macro.
proc insight data = concy;
scatter income water80 educat retired peop81 cpeop water81 *
income water80 educat retired peop81 cpeop water81;
run;
page 115 Figure 4.2 Scatterplot matrix for data from 122 countries, using the
nations data set.
proc insight data = nations;
scatter encon85 popgro85 fert84 birthr85 * encon85 popgro85 fert84 birthr85;
run;
Residual Versus Predicted Y Plots
page 116 Figure 4.3 Residuals (e) versus predicted values (Y-hat) from regression of 1981
household water use on seven predictors.
proc reg data=concy;
model water81 = income water80 educat retired peop81 cpeop peop80;
output out=out1(keep=case e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 740477522 123412920 171.08 <.0001
Error 489 352761188 721393
Corrected Total 495 1093238710
Root MSE 849.34859 R-Square 0.6773
Dependent Mean 2298.38710 Adj R-Sq 0.6734
Coeff Var 36.95411
NOTE: Model is not full rank. Least-squares solutions for the parameters are not unique. Some
statistics will be misleading. A reported DF of 0 or B means that the estimate is biased.
NOTE: The following parameters have been set to 0, since the variables are a linear combination
of other variables as shown.
peop80 = peop81 - cpeop
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 242.22043 206.86382 1.17 0.2422
income 1 20.96699 3.46372 6.05 <.0001
water80 1 0.49194 0.02635 18.67 <.0001
educat 1 -41.86552 13.22031 -3.17 0.0016
retired 1 189.18433 95.02142 1.99 0.0470
peop81 B 248.19702 28.72480 8.64 <.0001
cpeop B 96.45360 80.51903 1.20 0.2315
peop80 0 0 . . .
proc reg data=concy;
model water81 = income water80 educat retired peop81 cpeop peop80;
output out=out2(keep=case yhat) predicted=yhat;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 740477522 123412920 171.08 <.0001
Error 489 352761188 721393
Corrected Total 495 1093238710
Root MSE 849.34859 R-Square 0.6773
Dependent Mean 2298.38710 Adj R-Sq 0.6734
Coeff Var 36.95411
NOTE: Model is not full rank. Least-squares solutions for the parameters are not unique. Some
statistics will be misleading. A reported DF of 0 or B means that the estimate is biased.
NOTE: The following parameters have been set to 0, since the variables are a linear combination
of other variables as shown.
peop80 = peop81 - cpeop
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 242.22043 206.86382 1.17 0.2422
income 1 20.96699 3.46372 6.05 <.0001
water80 1 0.49194 0.02635 18.67 <.0001
educat 1 -41.86552 13.22031 -3.17 0.0016
retired 1 189.18433 95.02142 1.99 0.0470
peop81 B 248.19702 28.72480 8.64 <.0001
cpeop B 96.45360 80.51903 1.20 0.2315
peop80 0 0 . . .
data concordall;
merge concord1 out1 out2;
by case;
label e = . ;
label yhat = . . ;
proc univariate data=concordall;
var yhat e;
run;
The UNIVARIATE Procedure
Variable: yhat (predicted value)
Moments
N 496 Sum Weights 496
Mean 2298.3871 Sum Observations 1140000
Std Deviation 1223.07571 Variance 1495914.19
Skewness 1.02246077 Kurtosis 1.53522546
Uncorrected SS 3360638812 Corrected SS 740477522
Coeff Variation 53.214522 Std Error Mean 54.9177205
Basic Statistical Measures
Location Variability
Mean 2298.387 Std Deviation 1223
Median 2024.846 Variance 1495914
Mode 1252.343 Range 7574
Interquartile Range 1643
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 41.85147 Pr > |t| <.0001
Sign M 248 Pr >= |M| <.0001
Signed Rank S 61628 Pr >= |S| <.0001
Quantiles (Definition 5)
Quantile Estimate
100% Max 7837.047
99% 6242.199
95% 4425.504
90% 3884.347
75% Q3 3036.301
50% Median 2024.846
25% Q1 1392.983
10% 902.298
5% 649.121
1% 359.403
0% Min 262.776
The UNIVARIATE Procedure
Variable: yhat (predicted value)
Extreme Observations
------Lowest----- -----Highest-----
Value Obs Value Obs
262.776 100 6242.20 232
296.707 424 6697.20 194
345.901 375 6736.44 451
353.493 366 7321.02 62
359.403 330 7837.05 94
The UNIVARIATE Procedure
Variable: e (residual)
Moments
N 496 Sum Weights 496
Mean 0 Sum Observations 0
Std Deviation 844.185326 Variance 712648.864
Skewness 1.18637008 Kurtosis 6.77888563
Uncorrected SS 352761188 Corrected SS 352761188
Coeff Variation . Std Error Mean 37.9050401
Basic Statistical Measures
Location Variability
Mean 0.0000 Std Deviation 844.18533
Median -69.4956 Variance 712649
Mode 22.7855 Range 9075
Interquartile Range 814.02638
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 0 Pr > |t| 1.0000
Sign M -18 Pr >= |M| 0.1160
Signed Rank S -4887 Pr >= |S| 0.1261
Quantiles (Definition 5)
Quantile Estimate
100% Max 5037.9871
99% 3315.5848
95% 1367.2257
90% 906.9871
75% Q3 365.3865
50% Median -69.4956
25% Q1 -448.6399
10% -828.8270
5% -1212.3343
1% -1870.9171
0% Min -4037.0471
The UNIVARIATE Procedure
Variable: e (residual)
Extreme Observations
------Lowest----- -----Highest-----
Value Obs Value Obs
-4037.05 94 3315.58 118
-2224.40 494 3687.12 125
-1938.20 163 4112.44 124
-1883.80 133 4512.28 80
-1870.92 362 5037.99 85
To draw the horizontal boxplot, we need to use an annotated data set. The code below
tells SAS where to draw each of the lines for the two boxplots. These numbers were
obtained from the proc univariate immediately above this data step.
data anno_call1;
length function color $8;
retain xsys ysys '2' size 1 color 'green';
function='move'; x=262.776; y=6000; output; * begin left line ;
function='draw'; x=1392.983; y=6000; output; * end left line ;
function='poly'; x=1392.983; y=6100; output; * upper left corner of box ;
function='polycont'; x=1392.983; y=5900; output; * lower left corner ;
function='polycont'; x=3036.301; y=5900; output; * lower right corner of box ;
function='polycont'; x=3036.301; y=6100; output; * upper right corner of box ;
function='polycont'; x=1392.983; y=6100; output; * back to upper left corner ;
function='move'; x=2024.846; y=6100; output; * middle line of box ;
function='draw'; x=2024.846; y=5900; output;
function='move'; x=3036.301; y=6000; output; * begin right line ;
function='draw'; x=6242.199; y=6000; output; * end right line ;
* to draw the vertical boxplot ;
function='move'; x=8500; y=1586.42607; output; * begin top line ;
function='draw'; x=8500; y=365.3865; output; * end top line ;
function='poly'; x=8400; y=365.3865; output; * upper left corner of box ;
function='polycont'; x=8600; y=365.3865; output; * upper right corner ;
function='polycont'; x=8600; y=-448.6399; output; * lower right corner of box ;
function='polycont'; x=8400; y=-448.6399; output; * lower left corner ;
function='polycont'; x=8400; y=365.3865; output; * back to upper left ;
function='move'; x=8400; y=-69.4956; output; * middle line of box ;
function='draw'; x=8600; y=-69.4956; output;
function='move'; x=8500; y=-448.6399; output; * begin bottom line ;
function='draw'; x=8500; y=-1669.67947; output; * end bottom line ;
run;
symbol1 color=black interpol=r value=circle height=0.5;
axis1 order=(-4000 to 8000 by 2000);
axis2 order=(0 to 10000 by 2000);
proc gplot data=concordall;
plot e*yhat=1 / anno=anno_call1 vaxis=axis1 haxis=axis2;
run;
quit;
Figure 4.3 The interpol=r option is used in the first symbol statement and tells SAS to include the
regression line. Interpol can be shortened to i.
page 117 Figure 4.4 Absolute residuals |e| versus Y-hat, with band regression line
indicating heteroscedasticity (household water-use regression).
data concordalla;
set concordall;
abse=abs(e);
proc means min max data=concordalla;
var yhat;
run;
The MEANS Procedure
Analysis Variable : yhat predicted value
Minimum Maximum
----------------------------
262.7759103 7837.05
----------------------------
data newset;
set concordalla;
do i = 1 to 6;
if (i-1)*(7837.05-262.776)/6 + 262.776 <= yhat
< i*(7837.05-262.776)/6 + 262.776 then do;
a = i; output; end;
end;
run;
proc means median data=newset nway; /*find the median for x and y*/
class a;
var yhat abse;
output out=med median=ymed absemed;
run;
The MEANS Procedure
N
a Obs Variable Label Median
------------------------------------------------------------------
1 148 yhat predicted value 1122.77
abse 273.1849543
2 200 yhat predicted value 2033.12
abse 390.5594506
3 104 yhat predicted value 3367.23
abse 588.5223764
4 30 yhat predicted value 4292.81
abse 1084.30
5 9 yhat predicted value 5535.21
abse 1367.23
6 4 yhat predicted value 7028.73
abse 1721.27
------------------------------------------------------------------
proc sort data=med;
by a;
proc sort data=newset;
by a;
run;
data outset; /* merge it back to the original dataset */
merge newset med;
by a;
run;
symbol1 color=black value=circle height=0.5;
symbol2 c=red v=none i=join l=2;
axis1 order=(0 to 6000 by 1000);
axis2 order=(0 to 8000 by 2000);
proc gplot data=outset;
plot abse*yhat=1 absemed*ymed=2 / overlay vaxis=axis1 haxis=axis2;
run;
quit;
The line option (which can be abbreviated as l) tells SAS which type of line to use. SAS
has approximately 50 different line types that can be selected, and each one has a number.
To select a different type of line, simply replace the 2 with another line number.
Figure 4.4
Autocorrelation
page 119 Figure 4.5 Time plot of average daily water use by the city of Concord,
1970-1981, using the concord2 data set.
symbol1 color=black interpol=join value=none height=0.5;
axis1 order=(3.5 to 5.5 by 0.5);
axis2 order=(1 to 120 by 20);
proc gplot data=concord2;
plot H2Ouse*time=1 / href=127 lhref=2;
run;
quit;
The href option tells SAS to put a horizontal reference line at 127. The lhref
option tells SAS what kind of line to use. It is similar to the line option that was used above.
Figure 4.5
page 121 Figure 4.6 Correlogram showing autocorrelation of Concord water-use residuals,
at monthly lags 0-25.
proc autoreg data=concord2;
model H2Ouse = temp rain educ / nlag = 26;
ods output CorrGraph=concyautoreg;
run;
quit;
The AUTOREG Procedure
Dependent Variable H2Ouse
Ordinary Least Squares Estimates
SSE 17.2802336 DFE 133
MSE 0.12993 Root MSE 0.36045
SBC 124.821864 AIC 113.14194
Regress R-Square 0.3273 Total R-Square 0.3273
Durbin-Watson 0.5349
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 3.8280 0.1006 38.03 <.0001
temp 1 0.0129 0.001698 7.57 <.0001
rain 1 -0.0474 0.0212 -2.23 0.0271
educ 1 -0.2470 0.1135 -2.18 0.0313
Estimates of Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0 0.1261 1.000000 | |********************|
1 0.0921 0.730231 | |*************** |
2 0.0597 0.473521 | |********* |
3 0.0435 0.345115 | |******* |
4 0.0580 0.459549 | |********* |
5 0.0706 0.559339 | |*********** |
6 0.0744 0.589674 | |************ |
7 0.0582 0.461684 | |********* |
8 0.0354 0.280885 | |****** |
9 0.0194 0.153916 | |*** |
10 0.0302 0.239722 | |***** |
11 0.0535 0.424193 | |******** |
12 0.0612 0.485392 | |********** |
13 0.0430 0.340738 | |******* |
14 0.0193 0.152932 | |*** |
15 0.0164 0.129701 | |*** |
16 0.0272 0.215724 | |**** |
17 0.0428 0.339531 | |******* |
18 0.0466 0.369486 | |******* |
19 0.0343 0.271671 | |***** |
20 0.0108 0.085549 | |** |
21 -0.00238 -0.018880 | | |
22 0.00370 0.029327 | |* |
23 0.0250 0.198215 | |**** |
24 0.0329 0.260869 | |***** |
25 0.0204 0.161734 | |*** |
26 -0.00063 -0.004964 | | |
The AUTOREG Procedure
Preliminary MSE 0.0348
Estimates of Autoregressive Parameters
Standard
Lag Coefficient Error t Value
1 -0.633558 0.096645 -6.56
2 -0.043799 0.114254 -0.38
3 0.093387 0.113960 0.82
4 -0.335057 0.114273 -2.93
5 0.016375 0.117644 0.14
6 -0.048498 0.117465 -0.41
7 0.025855 0.117467 0.22
8 0.048794 0.117482 0.42
9 0.166974 0.117203 1.42
10 -0.039854 0.118284 -0.34
11 -0.164261 0.118311 -1.39
12 -0.062547 0.118359 -0.53
13 0.079678 0.117840 0.68
14 0.130513 0.117840 1.11
15 -0.160535 0.118359 -1.36
16 0.029807 0.118311 0.25
17 -0.025415 0.118284 -0.21
18 -0.096891 0.117203 -0.83
19 0.017487 0.117482 0.15
20 0.047749 0.117467 0.41
21 0.069170 0.117465 0.59
22 0.169159 0.117644 1.44
23 -0.032654 0.114273 -0.29
24 -0.095382 0.113960 -0.84
25 -0.063571 0.114254 -0.56
26 0.024134 0.096645 0.25
Yule-Walker Estimates
SSE 4.4304032 DFE 107
MSE 0.04141 Root MSE 0.20348
SBC 71.6729358 AIC -15.926492
Regress R-Square 0.6497 Total R-Square 0.8275
Durbin-Watson 2.0353
The AUTOREG Procedure
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 3.7674 0.1455 25.89 <.0001
temp 1 0.0133 0.000971 13.73 <.0001
rain 1 -0.0406 0.009274 -4.37 <.0001
educ 1 -0.2134 0.1642 -1.30 0.1966
axis1 order =(-.2 to 1 by .2) label=(r=0 a=90);
axis2 order = (0 to 26 by 2);
symbol1 color=green i=needle v=none width=20;
title 'Figure 4.6';
proc gplot data=concyautoreg;
format Autocorr 4.2;
plot Autocorr*Lag=1/ haxis=axis2 vaxis=axis1 hminor=0 vminor=0 vref=.16 lvref=2;
label Autocorr='Autocorrelation';
run;
quit;
The hminor and vminor options instruct SAS regarding tick marks.
The hminor=0 option
means that no tick marks are to appear on the horizontal axis, and the vminor=0
option means that no tick marks are to appear on the vertical axis. In the axis1 order
statement, the label=(r=0 a=90) means that the axis label will be turned 90 degrees.
This greatly improves the appearance of the graph.
page 122 Figure 4.7 Time plot of Concord water-use residuals.
proc reg data=concord2;
model H2Ouse = temp rain educ;
output out=outx(keep=time e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: H2Ouse
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 8.40906 2.80302 21.57 <.0001
Error 133 17.28023 0.12993
Corrected Total 136 25.68929
Root MSE 0.36045 R-Square 0.3273
Dependent Mean 4.23496 Adj R-Sq 0.3122
Coeff Var 8.51138
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 3.82800 0.10064 38.03 <.0001
temp 1 0.01286 0.00170 7.57 <.0001
rain 1 -0.04743 0.02123 -2.23 0.0271
educ 1 -0.24698 0.11348 -2.18 0.0313
symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=outx;
plot e*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;
Figure 4.7
page 122 Figure 4.8 Time plots of Concord water-use residuals, showing effects of repeated
smoothing by running means of span 3. Note that the first of the four graphs is the same as
the graph above.
proc reg data=concord2;
model H2Ouse = temp rain educ;
output out=outx(keep=time e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: H2Ouse
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 8.40906 2.80302 21.57 <.0001
Error 133 17.28023 0.12993
Corrected Total 136 25.68929
Root MSE 0.36045 R-Square 0.3273
Dependent Mean 4.23496 Adj R-Sq 0.3122
Coeff Var 8.51138
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 3.82800 0.10064 38.03 <.0001
temp 1 0.01286 0.00170 7.57 <.0001
rain 1 -0.04743 0.02123 -2.23 0.0271
educ 1 -0.24698 0.11348 -2.18 0.0313
symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=outx;
plot e*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;
proc reg data=concord2;
model H2Ouse = temp rain educ;
output out=outx(keep= e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: H2Ouse
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 8.40906 2.80302 21.57 <.0001
Error 133 17.28023 0.12993
Corrected Total 136 25.68929
Root MSE 0.36045 R-Square 0.3273
Dependent Mean 4.23496 Adj R-Sq 0.3122
Coeff Var 8.51138
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 3.82800 0.10064 38.03 <.0001
temp 1 0.01286 0.00170 7.57 <.0001
rain 1 -0.04743 0.02123 -2.23 0.0271
educ 1 -0.24698 0.11348 -2.18 0.0313
data outx1;
set outx;
id=_n_;
run;
proc loess data=outx1;
model e=id / direct smooth=0.05;
ods output OutputStatistics=ENSOstats;
run;
The LOESS Procedure
Independent Variable Scaling
Scaling applied: None
Statistic id
Minimum Value 1.00000
Maximum Value 137.00000
The LOESS Procedure
Smoothing Parameter: 0.05
Dependent Variable: e
Fit Summary
Fit Method Direct
Number of Observations 137
Degree of Local Polynomials 1
Smoothing Parameter 0.05000
Points in Local Neighborhood 6
Residual Sum of Squares 2.98454
symbol1 color=black interpol=join value=none width=2;
proc gplot data=ENSOstats;
plot pred*id=1;
run;
quit;
data concord21;
set outx;
time=_n_;
a1=lag(e);
a2=lag(a1);
e1=mean(a2, a1, e);
b1=lag(e1);
b2=lag(b1);
e2=mean(b2, b1, e1);
c1=lag(e2);
c2=lag(c1);
e3=mean(c2, c1, e2);
d1=lag(e3);
d2=lag(d1);
e4=mean(d2, d1, e3);
f1=lag(e4);
f2=lag(f1);
e5=mean(f2, f1, e4);
run;
goptions reset=all;
filename outfile 'e:\rwgsas4j.gif';
goptions gsfmode=replace gsfname=outfile device=gif373;
symbol1 color=black interpol=join value=none;
axis1 order=(-.8 to .8 by 0.2);
axis2 order=(0 to 140 by 20);
proc gplot data=concord21;
plot e1*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;
proc gplot data=concord21;
plot e2*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;
proc gplot data=concord21;
plot e5*time=1 / haxis=axis2 vaxis=axis1 vref=0 hminor=1 vminor=0;
run;
quit;
4Nonnormality
page 124 Figure 4.9 Four views showing nonnormality of residuals from regression of 1981
household water use on six predictors.
proc reg data=concy;
model water81 = income water80 educat retired peop81 cpeop;
output out=out3(keep=case e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 740477522 123412920 171.08 <.0001
Error 489 352761188 721393
Corrected Total 495 1093238710
Root MSE 849.34859 R-Square 0.6773
Dependent Mean 2298.38710 Adj R-Sq 0.6734
Coeff Var 36.95411
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 242.22043 206.86382 1.17 0.2422
income 1 20.96699 3.46372 6.05 <.0001
water80 1 0.49194 0.02635 18.67 <.0001
educat 1 -41.86552 13.22031 -3.17 0.0016
retired 1 189.18433 95.02142 1.99 0.0470
peop81 1 248.19702 28.72480 8.64 <.0001
cpeop 1 96.45360 80.51903 1.20 0.2315
proc univariate data=out3 noprint;
var e;
histogram / noframe normal(color=red) cfill=grey midpoints=-4000 to 5000 by 750;
run;
The UNIVARIATE Procedure
Fitted Distribution for e
Parameters for Normal Distribution
Parameter Symbol Estimate
Mean Mu 0
Std Dev Sigma 844.1853
Goodness-of-Fit Tests for Normal Distribution
Test ---Statistic---- -----p Value-----
Kolmogorov-Smirnov D 0.09008163 Pr > D <0.010
Cramer-von Mises W-Sq 1.34942807 Pr > W-Sq <0.005
Anderson-Darling A-Sq 8.06505238 Pr > A-Sq <0.005
Quantiles for Normal Distribution
---------Quantile--------
Percent Observed Estimated
1.0 -1870.9171 -1963.868737
5.0 -1212.3343 -1388.561295
10.0 -828.8270 -1081.867026
25.0 -448.6399 -569.394349
50.0 -69.4956 -0.000000
75.0 365.3865 569.394349
90.0 906.9871 1081.867026
95.0 1367.2257 1388.561295
99.0 3315.5848 1963.868737
Unlike Stata that uses the bin option to determine the size of the bins of the histogram
SAS asks for the midpoints of the bins. That is the purpose of the midpoints option
shown above.
Figure 4.9 histogram
data concz;
set out3;
cvar=2;
proc boxplot data=concz;
plot e*cvar / boxstyle=schematic
cboxes=green idsymbol=circle noframe boxwidth=15 vaxis=-4100 to 5100 by 2300;
run;
quit;
Figure 4.9 boxplot
Below is the code for a symmetry plot - SAS does not have a symmetry plot feature,
so you have to do it by hand.
proc reg data=concy;
model water81 = income water80 educat retired peop81 cpeop;
output out=outa (keep=case water81 e) residual=e;
run;
quit;
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 740477522 123412920 171.08 <.0001
Error 489 352761188 721393
Corrected Total 495 1093238710
Root MSE 849.34859 R-Square 0.6773
Dependent Mean 2298.38710 Adj R-Sq 0.6734
Coeff Var 36.95411
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 242.22043 206.86382 1.17 0.2422
income 1 20.96699 3.46372 6.05 <.0001
water80 1 0.49194 0.02635 18.67 <.0001
educat 1 -41.86552 13.22031 -3.17 0.0016
retired 1 189.18433 95.02142 1.99 0.0470
peop81 1 248.19702 28.72480 8.64 <.0001
cpeop 1 96.45360 80.51903 1.20 0.2315
proc univariate data=outa noprint;
var e;
output out = stats1 median = med81 n = n81 ;
data stats2;
set stats1; evodd81 = mod(n81,2);
/* even/odd flag */
call symput('evodd81',evodd81);
call symput('med81',med81);
call symput('n81',n81);
proc sort data=outa
out=sorted81(keep=e);
by e;
data above81(drop=b) below81(drop=a);
set sorted81; i = _n_;
/* n is even */
if evodd81 = 0 then do;
if i <= &n81 / 2 then do;
b = &med81 - e; output below81;
end;
else do;
a = e - &med81;
output above81;
end;
end;
/* n is odd */
else do;
if i <= (&n81 + 1)/2 then do;
b = &med81 - e; output below81;
end;
if i >= (&n81 + 1)/2 then do;
a = e - &med81; output above81;
end;
end;
proc sort data=above81;
by descending i;
data ab;
merge above81 below81;
/* n is even */
if &evodd81 = 0 then do;
if i = 1 then x = min(a,b);
else if i = &n81 / 2 then x = max(a,b); y=x;
end;
/* n is odd */
else do;
if i = 1 then x = min(a,b);
else if i = (&n81 + 1)/2 then x = max(a,b);
y=x;
end;
axis1 order=(0 to 6000 by 2000) label=(angle=90 height=.75 'Distance above median');
axis2 order=(0,2000,4000) label=('Distance below median');
symbol1 interpol=none value=circle color=black height=.5; symbol2 interpol=join value=none color=red;
proc gplot data=ab; plot a*b y*x /
vaxis=axis1 vminor=0
haxis=axis2 hminor=0
noframe overlay;
run;
quit;
Figure 4.9 symmetry plot
proc univariate data=outa noprint;
var e;
probplot / normal(mu=est sigma=est color=red) noframe;
run;
quit;
Figure 4.9 quantile-normal plot
Influence Analysis
page 127 Table 4.3 Summary statistics for DFBETAS of coefficients in household water-use
regression of Equation [4.3].
proc reg data=concy;
model water81 = income water80 educat retired peop81 cpeop /influence;
ods output OutputStatistics=cydfbetas;
run;
quit;
proc means data=cydfbetas;
var DFB_income DFB_water80 DFB_educat DFB_retired DFB_peop81 DFB_cpeop;
run;
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 6 740477522 123412920 171.08 <.0001
Error 489 352761188 721393
Corrected Total 495 1093238710
Root MSE 849.34859 R-Square 0.6773
Dependent Mean 2298.38710 Adj R-Sq 0.6734
Coeff Var 36.95411
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 242.22043 206.86382 1.17 0.2422
income 1 20.96699 3.46372 6.05 <.0001
water80 1 0.49194 0.02635 18.67 <.0001
educat 1 -41.86552 13.22031 -3.17 0.0016
retired 1 189.18433 95.02142 1.99 0.0470
peop81 1 248.19702 28.72480 8.64 <.0001
cpeop 1 96.45360 80.51903 1.20 0.2315
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
1 -388.8667 -0.4590 0.0066 1.0180 -0.0373
2 -1667 -1.9899 0.0215 0.9797 -0.2948
3 343.6106 0.4076 0.0165 1.0290 0.0528
4 -779.8772 -0.9262 0.0174 1.0198 -0.1234
5 1335 1.5897 0.0193 0.9977 0.2232
6 -154.2695 -0.1824 0.0108 1.0250 -0.0191
7 764.1568 0.9038 0.0093 1.0121 0.0878
8 488.5489 0.5799 0.0174 1.0274 0.0771
9 318.2554 0.3759 0.0083 1.0208 0.0343
10 439.8363 0.5205 0.0117 1.0225 0.0567
11 1078 1.2744 0.0073 0.9984 0.1093
12 800.0813 0.9481 0.0130 1.0146 0.1087
13 -367.3797 -0.4335 0.0059 1.0177 -0.0333
14 1052 1.2594 0.0316 1.0240 0.2276
15 -523.4685 -0.6250 0.0289 1.0388 -0.1078
16 -143.1716 -0.1690 0.0075 1.0217 -0.0147
17 -165.9163 -0.1960 0.0091 1.0232 -0.0188
18 -738.2989 -0.8745 0.0124 1.0160 -0.0981
19 557.5599 0.6607 0.0140 1.0224 0.0787
20 -55.1810 -0.0652 0.0087 1.0233 -0.0061
21 -694.7070 -0.8207 0.0074 1.0121 -0.0707
22 423.7686 0.4996 0.0040 1.0149 0.0317
23 -243.7578 -0.2875 0.0054 1.0187 -0.0212
24 -450.8112 -0.5349 0.0167 1.0275 -0.0698
25 2390 2.8678 0.0232 0.9238 0.4415
26 -431.9259 -0.5101 0.0077 1.0185 -0.0451
27 500.0761 0.5906 0.0075 1.0170 0.0514
28 348.6592 0.4125 0.0115 1.0237 0.0445
29 -782.9470 -0.9236 0.0041 1.0062 -0.0592
30 -642.0676 -0.7609 0.0138 1.0201 -0.0899
31 -1441 -1.7189 0.0222 0.9945 -0.2590
32 939.7894 1.1136 0.0122 1.0089 0.1240
33 11.9625 0.0142 0.0132 1.0280 0.0016
34 668.9890 0.7957 0.0210 1.0268 0.1164
35 199.3090 0.2351 0.0053 1.0190 0.0171
36 1379 1.6419 0.0187 0.9946 0.2264
37 99.2552 0.1176 0.0139 1.0285 0.0140
38 -1224 -1.4555 0.0180 1.0021 -0.1968
39 196.4742 0.2324 0.0110 1.0249 0.0245
40 -427.0224 -0.5044 0.0080 1.0188 -0.0452
41 -153.3359 -0.1817 0.0153 1.0297 -0.0226
42 22.7855 0.0269 0.0095 1.0241 0.0026
43 527.2992 0.6253 0.0155 1.0246 0.0785
44 327.0076 0.3861 0.0075 1.0199 0.0336
45 1077 1.2745 0.0089 1.0000 0.1207
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
1 0.0146 -0.0077 -0.0067 -0.0206 0.0073 0.0102 -0.0022
2 0.1725 -0.1941 0.0024 -0.0976 -0.0588 -0.0455 0.0183
3 -0.0142 -0.0051 -0.0021 0.0116 0.0006 0.0242 0.0349
4 -0.0333 -0.0393 0.0115 0.0409 -0.0504 0.0192 0.0792
5 -0.0811 0.1069 0.0693 0.0882 -0.0085 -0.1138 0.0158
6 -0.0033 0.0042 0.0120 0.0014 0.0048 -0.0138 0.0021
7 -0.0233 0.0206 0.0260 0.0026 0.0742 0.0037 0.0061
8 -0.0508 -0.0077 0.0076 0.0580 0.0433 -0.0041 0.0063
9 0.0203 -0.0124 -0.0128 -0.0129 -0.0152 0.0134 -0.0011
10 -0.0222 -0.0023 0.0014 0.0420 -0.0150 -0.0200 0.0044
11 0.0777 -0.0487 0.0319 -0.0464 -0.0585 -0.0230 0.0113
12 -0.0733 -0.0164 -0.0236 0.0825 -0.0034 0.0523 -0.0057
13 0.0125 -0.0083 0.0044 -0.0078 0.0007 -0.0177 0.0027
14 -0.0668 -0.0782 -0.0496 0.0581 -0.0074 0.1685 -0.1357
15 0.0046 -0.0127 0.0213 0.0230 -0.0117 -0.0749 -0.0453
16 -0.0050 0.0055 0.0081 0.0010 0.0063 -0.0072 0.0008
17 -0.0057 -0.0054 0.0015 0.0049 -0.0105 0.0061 -0.0018
18 -0.0654 -0.0579 0.0366 0.0702 0.0244 0.0040 0.0049
19 -0.0361 0.0041 0.0438 0.0226 0.0572 -0.0073 0.0084
20 -0.0021 0.0013 0.0011 0.0015 -0.0031 -0.0005 -0.0004
21 -0.0332 -0.0111 0.0456 0.0279 0.0230 -0.0311 0.0068
22 0.0117 0.0087 -0.0091 -0.0117 -0.0103 0.0095 -0.0018
23 -0.0025 0.0004 -0.0016 -0.0066 0.0106 0.0117 -0.0024
24 0.0308 -0.0245 0.0318 -0.0305 -0.0416 -0.0093 0.0010
25 -0.0747 -0.1338 0.0144 -0.0103 0.0201 0.3549 -0.0364
26 -0.0031 -0.0064 0.0141 0.0025 -0.0308 -0.0038 -0.0019
27 0.0357 0.0223 -0.0096 -0.0263 -0.0226 -0.0222 0.0019
28 -0.0008 -0.0019 -0.0077 0.0221 -0.0191 -0.0223 0.0039
29 -0.0236 0.0190 0.0184 -0.0025 0.0360 -0.0009 -0.0020
30 -0.0551 0.0080 0.0212 0.0517 -0.0323 -0.0086 -0.0036
31 0.0389 -0.0404 0.1013 0.0111 -0.1391 -0.1440 0.1759
32 0.1150 -0.0297 -0.0184 -0.0737 -0.0698 -0.0290 0.0073
33 0.0010 -0.0002 -0.0002 -0.0010 0.0006 0.0001 0.0001
34 -0.0199 -0.0249 -0.0201 0.0413 0.0452 0.0029 0.0798
35 0.0063 -0.0084 -0.0054 0.0018 -0.0102 0.0012 0.0006
36 -0.0007 0.1695 -0.0287 -0.0338 0.1275 -0.0656 0.0068
37 0.0022 0.0034 -0.0038 -0.0031 -0.0023 0.0041 -0.0117
38 0.0922 -0.1087 -0.0512 -0.0782 -0.0092 0.0623 -0.0066
39 -0.0123 -0.0065 -0.0021 0.0207 -0.0060 -0.0006 0.0010
40 -0.0100 0.0057 0.0112 0.0058 -0.0263 -0.0046 -0.0029
41 0.0111 0.0086 0.0083 -0.0178 0.0044 -0.0081 0.0006
42 0.0009 -0.0007 -0.0004 -0.0002 0.0010 -0.0005 0.0003
43 0.0159 -0.0154 0.0015 -0.0058 0.0253 -0.0097 -0.0499
44 0.0071 -0.0055 -0.0026 -0.0045 0.0205 0.0008 0.0031
45 0.0173 -0.0143 0.0521 -0.0195 0.0753 -0.0277 0.0178
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
46 22.7855 0.0269 0.0095 1.0241 0.0026
47 -914.4225 -1.0854 0.0157 1.0134 -0.1371
48 395.6209 0.4684 0.0126 1.0241 0.0529
49 517.8713 0.6131 0.0123 1.0215 0.0684
50 231.4842 0.2732 0.0067 1.0202 0.0224
51 -1045 -1.2369 0.0104 1.0029 -0.1267
52 -372.9229 -0.4405 0.0080 1.0198 -0.0397
53 -586.0330 -0.6912 0.0046 1.0122 -0.0470
54 -321.0289 -0.3789 0.0067 1.0191 -0.0310
55 0.5991 0.000707 0.0067 1.0213 0.0001
56 -349.1211 -0.4127 0.0099 1.0221 -0.0413
57 77.2007 0.0912 0.0082 1.0227 0.0083
58 -313.8129 -0.3722 0.0164 1.0293 -0.0480
59 -786.5014 -0.9309 0.0108 1.0129 -0.0973
60 157.7162 0.1862 0.0079 1.0220 0.0166
61 361.7777 0.4286 0.0142 1.0263 0.0514
62 2079 2.5265 0.0510 0.9760 0.5859
63 -721.8686 -0.8556 0.0138 1.0179 -0.1013
64 919.1880 1.0897 0.0132 1.0107 0.1262
65 -968.1694 -1.1786 0.0638 1.0622 -0.3077
66 103.3428 0.1221 0.0088 1.0232 0.0115
67 -883.5449 -1.0443 0.0076 1.0064 -0.0914
68 2003 2.4177 0.0391 0.9713 0.4875
69 -1074 -1.2761 0.0170 1.0082 -0.1679
70 1529 1.8436 0.0424 1.0091 0.3878
71 635.0666 0.7506 0.0086 1.0150 0.0699
72 321.9857 0.3818 0.0156 1.0284 0.0481
73 955.8874 1.1364 0.0187 1.0148 0.1568
74 149.2690 0.1762 0.0074 1.0215 0.0152
75 65.9999 0.0781 0.0130 1.0277 0.0090
76 -331.3901 -0.3914 0.0080 1.0204 -0.0352
77 -59.5560 -0.0702 0.0053 1.0198 -0.0051
78 357.6185 0.4245 0.0178 1.0302 0.0572
79 2565 3.0761 0.0197 0.9046 0.4357
80 4512 5.4938 0.0091 0.6726 0.5256
81 409.9462 0.4842 0.0079 1.0191 0.0432
82 1506 1.7846 0.0079 0.9770 0.1596
83 -78.7396 -0.0936 0.0220 1.0372 -0.0141
84 -456.0644 -0.5384 0.0066 1.0170 -0.0440
85 5038 6.1889 0.0114 0.6046 0.6632
86 -494.4666 -0.5851 0.0112 1.0209 -0.0623
87 -1216 -1.4516 0.0253 1.0099 -0.2340
88 -113.8159 -0.1348 0.0143 1.0289 -0.0162
89 237.8361 0.2805 0.0051 1.0185 0.0200
90 952.0715 1.1270 0.0101 1.0063 0.1140
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
46 0.0009 -0.0007 -0.0004 -0.0002 0.0010 -0.0005 0.0003
47 0.0894 -0.0666 0.0235 -0.0669 -0.0192 -0.0427 0.0108
48 -0.0114 0.0330 -0.0062 -0.0047 0.0423 0.0075 -0.0006
49 0.0490 -0.0388 -0.0125 -0.0159 -0.0418 -0.0106 0.0050
50 -0.0107 -0.0015 -0.0066 0.0149 -0.0043 0.0073 -0.0008
51 -0.0280 -0.0774 0.0405 0.0631 0.0025 -0.0540 0.0147
52 -0.0128 0.0002 -0.0043 0.0136 -0.0247 0.0038 -0.0041
53 -0.0347 0.0055 0.0101 0.0205 0.0275 0.0029 -0.0014
54 -0.0139 -0.0120 0.0132 0.0050 0.0141 0.0103 -0.0005
55 0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000
56 -0.0279 0.0056 0.0238 0.0106 0.0234 0.0033 -0.0003
57 0.0003 0.0016 0.0001 -0.0020 0.0067 0.0017 0.0003
58 0.0223 0.0084 0.0265 -0.0340 0.0077 -0.0197 0.0030
59 -0.0073 -0.0260 0.0481 0.0207 -0.0652 -0.0393 0.0038
60 -0.0028 -0.0024 -0.0011 0.0103 -0.0068 -0.0061 0.0014
61 -0.0253 -0.0213 0.0067 0.0237 0.0329 0.0214 0.0022
62 -0.1215 -0.1304 0.2451 -0.0547 0.0885 0.3393 -0.0218
63 0.0572 -0.0441 0.0367 -0.0563 -0.0019 -0.0218 0.0071
64 -0.0242 -0.0808 -0.0312 0.0838 -0.0490 0.0166 0.0046
65 0.0596 -0.2482 0.0490 0.0616 -0.1752 -0.0553 -0.0887
66 -0.0043 -0.0011 0.0012 0.0051 0.0080 -0.0008 0.0012
67 -0.0070 0.0180 0.0167 -0.0043 -0.0560 -0.0075 -0.0072
68 -0.0978 0.1264 0.2491 -0.0952 0.2785 0.0635 -0.2118
69 0.0093 -0.1104 0.0850 0.0155 -0.1000 -0.0167 0.0067
70 0.0440 -0.1120 0.0249 0.0007 -0.0493 0.0409 0.3507
71 0.0137 -0.0277 0.0072 -0.0039 0.0367 -0.0014 0.0085
72 0.0141 0.0370 -0.0273 -0.0176 -0.0061 0.0017 -0.0042
73 0.0496 -0.0694 0.0108 0.0161 -0.0647 -0.0490 0.1201
74 0.0111 0.0038 -0.0060 -0.0067 -0.0079 -0.0045 0.0003
75 0.0061 -0.0045 -0.0005 -0.0012 -0.0057 -0.0040 0.0011
76 -0.0250 0.0170 0.0015 0.0075 0.0230 0.0113 -0.0036
77 -0.0019 0.0009 0.0030 -0.0001 0.0028 -0.0007 0.0001
78 0.0308 -0.0123 -0.0101 -0.0099 -0.0290 -0.0157 -0.0355
79 0.0135 0.0212 0.1790 -0.1612 0.0361 0.1896 -0.0149
80 -0.0907 0.3825 -0.2014 0.0170 -0.0093 0.1030 -0.0475
81 0.0226 0.0290 -0.0089 -0.0249 -0.0107 -0.0071 -0.0010
82 0.0665 -0.1002 0.0208 0.0216 -0.0993 -0.0605 0.0216
83 0.0004 -0.0094 0.0047 -0.0020 0.0021 0.0054 0.0000
84 -0.0142 -0.0151 0.0286 0.0133 0.0116 -0.0184 0.0047
85 0.3854 0.3939 -0.2980 -0.3158 -0.2167 -0.1655 -0.0142
86 0.0417 0.0014 -0.0196 -0.0459 0.0023 0.0012 -0.0027
87 0.0669 -0.0073 -0.1522 -0.0633 0.0145 0.0775 0.1111
88 -0.0099 -0.0090 0.0044 0.0072 0.0058 0.0082 -0.0005
89 0.0101 0.0023 -0.0043 -0.0019 -0.0116 -0.0091 0.0014
90 0.0971 -0.0229 0.0265 -0.0792 -0.0519 -0.0234 0.0085
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
91 267.5371 0.3157 0.0063 1.0194 0.0252
92 -1367 -1.6233 0.0135 0.9903 -0.1901
93 58.2736 0.0688 0.0084 1.0230 0.0064
94 -4037 -5.0846 0.0817 0.7697 -1.5170
95 611.3653 0.7241 0.0127 1.0198 0.0822
96 99.2229 0.1177 0.0166 1.0313 0.0153
97 -1038 -1.2346 0.0187 1.0115 -0.1706
98 -390.0230 -0.4607 0.0079 1.0194 -0.0412
99 62.4404 0.0751 0.0442 1.0613 0.0162
100 337.2241 0.4006 0.0194 1.0321 0.0563
101 2178 2.5944 0.0117 0.9325 0.2818
102 71.1612 0.0840 0.0082 1.0227 0.0076
103 -1448 -1.7310 0.0263 0.9982 -0.2846
104 197.6948 0.2336 0.0093 1.0232 0.0227
105 -694.4760 -0.8216 0.0101 1.0149 -0.0831
106 63.2446 0.0753 0.0253 1.0407 0.0121
107 -101.5297 -0.1201 0.0121 1.0267 -0.0133
108 1367 1.6647 0.0615 1.0389 0.4262
109 134.0003 0.1581 0.0067 1.0209 0.0130
110 509.3545 0.6036 0.0142 1.0237 0.0725
111 -176.0944 -0.2077 0.0058 1.0197 -0.0159
112 -64.8879 -0.0772 0.0218 1.0369 -0.0115
113 251.3355 0.2971 0.0099 1.0233 0.0297
114 -295.3202 -0.3504 0.0173 1.0305 -0.0466
115 -767.2320 -0.9110 0.0171 1.0198 -0.1200
116 150.6509 0.1787 0.0172 1.0317 0.0236
117 -297.5814 -0.3510 0.0054 1.0181 -0.0258
118 3316 4.0942 0.0616 0.8534 1.0491
119 111.3602 0.1315 0.0080 1.0224 0.0118
120 490.2967 0.5808 0.0134 1.0233 0.0678
121 205.7678 0.2431 0.0091 1.0229 0.0233
122 582.5822 0.6898 0.0123 1.0201 0.0771
123 -295.6879 -0.3495 0.0096 1.0225 -0.0345
124 4112 5.0286 0.0268 0.7319 0.8348
125 3687 4.6465 0.0904 0.8237 1.4646
126 -252.3430 -0.2980 0.0079 1.0212 -0.0265
127 43.9022 0.0518 0.0060 1.0205 0.0040
128 -1156 -1.3830 0.0301 1.0177 -0.2436
129 -617.4949 -0.7295 0.0076 1.0145 -0.0639
130 149.0392 0.1764 0.0126 1.0269 0.0199
131 393.4716 0.4657 0.0122 1.0238 0.0518
132 171.7592 0.2025 0.0042 1.0181 0.0132
133 -1884 -2.2430 0.0142 0.9577 -0.2689
134 -223.7984 -0.2642 0.0076 1.0211 -0.0231
135 1551 1.8432 0.0131 0.9792 0.2124
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
91 0.0039 0.0005 -0.0098 0.0077 -0.0127 -0.0074 0.0011
92 0.0337 0.0513 -0.1129 -0.0026 0.0013 -0.0603 -0.0046
93 0.0021 0.0003 -0.0006 -0.0012 0.0033 -0.0018 0.0007
94 0.5610 0.0630 -1.3879 -0.3601 -0.1538 0.4554 -0.1647
95 -0.0588 -0.0184 0.0136 0.0630 -0.0008 0.0256 0.0001
96 -0.0045 -0.0006 0.0047 0.0026 -0.0004 0.0038 -0.0108
97 0.0491 -0.1034 0.0846 -0.0011 -0.0243 -0.1035 0.0264
98 -0.0070 0.0287 0.0088 -0.0075 0.0182 -0.0157 -0.0003
99 -0.0018 0.0035 -0.0050 0.0009 -0.0009 0.0045 -0.0151
100 -0.0096 -0.0208 -0.0119 0.0392 -0.0223 -0.0161 0.0043
101 -0.0979 0.0539 -0.1311 0.0520 0.0125 0.2238 -0.0404
102 -0.0018 0.0014 -0.0015 0.0018 0.0056 0.0002 0.0004
103 0.0968 0.1028 -0.1896 -0.1403 -0.1002 0.1248 -0.0517
104 -0.0084 -0.0044 0.0048 0.0104 0.0150 -0.0024 0.0028
105 -0.0628 0.0126 0.0142 0.0227 0.0519 0.0438 -0.0081
106 -0.0037 0.0089 -0.0008 0.0032 0.0002 -0.0041 0.0000
107 0.0095 -0.0001 0.0020 -0.0097 -0.0003 -0.0057 0.0007
108 -0.1422 -0.0402 -0.0009 -0.0126 0.2316 0.3556 -0.0373
109 0.0031 0.0095 -0.0013 -0.0038 -0.0026 -0.0031 -0.0001
110 0.0482 0.0043 0.0090 -0.0461 0.0250 -0.0234 0.0080
111 -0.0103 -0.0022 0.0031 0.0103 0.0056 -0.0038 0.0006
112 -0.0017 -0.0023 0.0005 0.0041 -0.0063 -0.0027 -0.0071
113 0.0129 -0.0081 0.0029 -0.0108 0.0139 -0.0011 0.0032
114 0.0300 0.0048 0.0017 -0.0355 -0.0254 -0.0006 -0.0030
115 0.0583 -0.0670 0.0069 -0.0157 -0.0976 -0.0353 0.0041
116 -0.0155 0.0011 -0.0010 0.0170 0.0139 -0.0003 0.0013
117 -0.0164 -0.0029 -0.0033 0.0079 0.0144 0.0156 -0.0029
118 -0.2691 0.9804 -0.1809 -0.0870 0.2371 0.0765 -0.0931
119 0.0074 0.0039 0.0036 -0.0059 -0.0047 -0.0075 0.0012
120 -0.0345 -0.0221 0.0044 0.0464 0.0363 -0.0000 0.0066
121 -0.0088 0.0049 0.0003 0.0081 0.0177 -0.0019 0.0018
122 -0.0277 0.0005 -0.0175 0.0556 -0.0210 -0.0177 0.0031
123 -0.0157 -0.0013 0.0081 0.0107 -0.0151 0.0067 -0.0030
124 -0.2240 0.1597 0.6845 0.0277 0.0880 -0.1629 0.0605
125 -0.1195 1.3404 0.2510 -0.3333 0.2546 -0.4263 -0.0218
126 -0.0190 -0.0067 0.0120 0.0114 0.0134 0.0069 -0.0003
127 -0.0014 -0.0012 0.0002 0.0016 -0.0006 0.0022 -0.0001
128 0.1349 -0.1338 -0.0612 -0.0878 -0.1492 0.0586 -0.0125
129 -0.0320 0.0156 -0.0416 0.0216 0.0260 0.0267 -0.0089
130 0.0044 0.0119 -0.0102 -0.0090 -0.0006 0.0097 -0.0027
131 -0.0089 -0.0224 -0.0014 0.0258 0.0203 -0.0090 0.0067
132 -0.0004 0.0027 -0.0045 0.0041 -0.0052 -0.0008 0.0000
133 0.1805 0.1032 -0.0508 -0.2097 0.0137 -0.0835 -0.0038
134 -0.0050 0.0036 0.0026 0.0031 -0.0140 -0.0009 -0.0020
135 0.0399 -0.1341 0.1030 -0.0236 -0.0525 0.0463 0.0130
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
136 389.9307 0.4617 0.0127 1.0244 0.0524
137 -69.2229 -0.0818 0.0090 1.0235 -0.0078
138 90.4051 0.1069 0.0105 1.0251 0.0110
139 -246.9667 -0.2922 0.0118 1.0253 -0.0320
140 1841 2.2223 0.0405 0.9853 0.4568
141 -484.4968 -0.5721 0.0071 1.0169 -0.0485
142 -152.5721 -0.1811 0.0177 1.0323 -0.0243
143 592.5429 0.7020 0.0133 1.0208 0.0814
144 -525.5644 -0.6202 0.0058 1.0148 -0.0475
145 -283.5739 -0.3345 0.0057 1.0186 -0.0254
146 -500.6267 -0.5909 0.0064 1.0159 -0.0474
147 894.3988 1.0676 0.0268 1.0254 0.1770
148 163.7760 0.1932 0.0061 1.0201 0.0151
149 330.9084 0.3925 0.0166 1.0293 0.0511
150 -342.1771 -0.4252 0.1038 1.1289 -0.1447
151 413.0855 0.4871 0.0047 1.0158 0.0336
152 -304.7599 -0.3600 0.0085 1.0212 -0.0332
153 -398.0820 -0.4699 0.0066 1.0179 -0.0382
154 502.9212 0.5955 0.0125 1.0221 0.0671
155 692.6423 0.8293 0.0336 1.0394 0.1546
156 -837.2812 -0.9931 0.0147 1.0152 -0.1215
157 -767.9189 -0.9070 0.0067 1.0093 -0.0744
158 -652.0787 -0.7718 0.0113 1.0173 -0.0824
159 -245.9645 -0.2902 0.0062 1.0195 -0.0229
160 -78.3371 -0.0932 0.0221 1.0372 -0.0140
161 -96.6999 -0.1142 0.0073 1.0217 -0.0098
162 -341.7275 -0.4039 0.0092 1.0215 -0.0390
163 -1938 -2.3278 0.0303 0.9683 -0.4116
164 -48.9875 -0.0579 0.0094 1.0240 -0.0056
165 -18.0317 -0.0213 0.0113 1.0261 -0.0023
166 -314.0228 -0.3723 0.0153 1.0282 -0.0464
167 207.9017 0.2471 0.0206 1.0349 0.0358
168 -413.1968 -0.4888 0.0111 1.0223 -0.0518
169 -520.7958 -0.6140 0.0040 1.0130 -0.0387
170 1478 1.7585 0.0164 0.9867 0.2269
171 -120.6418 -0.1428 0.0131 1.0276 -0.0165
172 -627.5333 -0.7447 0.0167 1.0235 -0.0969
173 -315.6008 -0.3756 0.0229 1.0361 -0.0575
174 173.5915 0.2051 0.0094 1.0234 0.0200
175 -1300 -1.5414 0.0109 0.9913 -0.1617
176 27.8590 0.0329 0.0057 1.0202 0.0025
177 -881.0514 -1.0415 0.0078 1.0066 -0.0921
178 154.6453 0.1830 0.0115 1.0258 0.0198
179 -557.1758 -0.6596 0.0119 1.0203 -0.0723
180 -104.6759 -0.1244 0.0206 1.0355 -0.0180
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
136 0.0148 -0.0025 -0.0101 -0.0012 -0.0214 -0.0074 -0.0407
137 -0.0014 0.0024 -0.0012 -0.0005 -0.0035 0.0026 -0.0013
138 0.0066 0.0066 -0.0041 -0.0055 -0.0037 -0.0033 -0.0001
139 -0.0022 -0.0234 0.0081 0.0003 0.0056 0.0115 0.0001
140 -0.0213 0.3854 0.0812 -0.1340 0.2470 -0.1182 0.0078
141 0.0072 -0.0191 0.0308 -0.0090 0.0076 -0.0193 0.0051
142 0.0160 -0.0046 0.0006 -0.0160 -0.0151 0.0011 -0.0012
143 0.0094 0.0295 0.0073 -0.0137 -0.0138 -0.0101 -0.0635
144 -0.0014 0.0064 0.0296 -0.0095 0.0165 -0.0239 0.0036
145 -0.0035 0.0167 -0.0069 -0.0033 0.0107 -0.0041 -0.0017
146 0.0100 -0.0300 0.0125 -0.0048 0.0029 -0.0086 0.0033
147 -0.0060 -0.0684 0.1412 0.0260 0.0530 -0.0883 0.0351
148 0.0117 -0.0012 0.0014 -0.0061 -0.0092 -0.0079 0.0017
149 -0.0016 0.0079 0.0063 -0.0095 0.0295 0.0084 -0.0347
150 0.0297 0.0249 0.0071 -0.0186 0.0012 -0.0634 0.1296
151 0.0183 -0.0170 -0.0007 -0.0038 -0.0210 -0.0027 0.0026
152 -0.0224 -0.0149 0.0126 0.0161 0.0142 0.0105 -0.0002
153 -0.0073 0.0185 0.0166 -0.0047 0.0166 -0.0178 0.0013
154 -0.0313 -0.0297 0.0007 0.0569 -0.0182 -0.0021 0.0041
155 0.0187 -0.0550 0.1400 0.0050 -0.0346 -0.0906 0.0276
156 -0.0098 -0.0091 -0.0071 0.0063 -0.0520 0.0238 0.0804
157 -0.0211 0.0223 -0.0097 0.0231 0.0186 -0.0347 0.0013
158 -0.0025 -0.0495 0.0218 0.0165 -0.0572 0.0013 -0.0007
159 -0.0148 -0.0012 0.0092 0.0055 0.0135 0.0069 -0.0009
160 0.0027 -0.0084 -0.0006 0.0005 -0.0018 -0.0008 -0.0080
161 -0.0068 -0.0040 0.0004 0.0051 0.0043 0.0049 -0.0006
162 -0.0133 0.0052 0.0097 0.0045 -0.0166 0.0063 -0.0038
163 -0.0078 0.2086 -0.1196 0.0155 0.0276 -0.1679 -0.2179
164 -0.0019 0.0013 0.0011 0.0005 -0.0023 0.0009 -0.0006
165 0.0011 -0.0004 0.0008 -0.0016 0.0004 -0.0000 0.0000
166 -0.0164 -0.0158 0.0145 0.0115 0.0141 0.0061 0.0347
167 -0.0203 -0.0124 -0.0055 0.0282 0.0151 0.0042 0.0021
168 0.0254 0.0020 0.0154 -0.0404 0.0107 -0.0020 -0.0001
169 0.0091 -0.0039 0.0097 -0.0136 0.0100 -0.0123 0.0015
170 -0.0503 -0.0496 0.1422 0.0775 0.1020 -0.1122 0.0426
171 0.0056 -0.0004 0.0054 -0.0115 0.0045 0.0029 -0.0004
172 0.0182 -0.0415 0.0149 -0.0054 -0.0055 -0.0211 -0.0624
173 -0.0137 -0.0377 0.0033 0.0190 0.0029 0.0141 -0.0341
174 0.0067 -0.0055 -0.0025 -0.0015 0.0079 -0.0039 0.0024
175 -0.0881 -0.0025 0.0200 0.0902 -0.0765 -0.0030 -0.0094
176 0.0012 -0.0012 0.0001 -0.0007 -0.0012 0.0006 0.0001
177 -0.0196 -0.0090 0.0239 0.0187 -0.0598 -0.0060 -0.0047
178 0.0013 0.0144 -0.0039 -0.0002 -0.0034 -0.0077 0.0001
179 -0.0384 -0.0509 0.0096 0.0378 0.0183 0.0301 -0.0009
180 -0.0095 -0.0010 0.0008 0.0095 -0.0048 0.0022 0.0103
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
181 -654.2538 -0.7738 0.0099 1.0158 -0.0775
182 -69.7684 -0.0824 0.0075 1.0220 -0.0072
183 -337.9932 -0.4007 0.0156 1.0282 -0.0505
184 -96.2014 -0.1135 0.0068 1.0212 -0.0094
185 -68.2045 -0.0806 0.0103 1.0249 -0.0082
186 -211.9686 -0.2506 0.0099 1.0237 -0.0251
187 -615.5789 -0.7291 0.0128 1.0198 -0.0832
188 311.9113 0.3701 0.0172 1.0301 0.0489
189 -532.6704 -0.6293 0.0079 1.0167 -0.0562
190 -105.9870 -0.1252 0.0089 1.0233 -0.0118
191 -657.4362 -0.7799 0.0156 1.0216 -0.0983
192 241.5939 0.2869 0.0186 1.0325 0.0395
193 40.3755 0.0478 0.0135 1.0283 0.0056
194 502.8014 0.6013 0.0320 1.0426 0.1093
195 547.6570 0.6470 0.0079 1.0163 0.0576
196 -92.6362 -0.1098 0.0161 1.0308 -0.0140
197 -34.9928 -0.0413 0.0056 1.0201 -0.0031
198 -335.9020 -0.4005 0.0268 1.0400 -0.0665
199 225.2630 0.2657 0.0056 1.0191 0.0200
200 -285.4190 -0.3369 0.0066 1.0196 -0.0275
201 -376.0955 -0.4439 0.0066 1.0183 -0.0361
202 -668.1564 -0.7894 0.0076 1.0131 -0.0691
203 855.1841 1.0118 0.0097 1.0095 0.1002
204 497.7022 0.5911 0.0186 1.0285 0.0814
205 -525.1719 -0.6198 0.0061 1.0150 -0.0484
206 -555.8710 -0.6566 0.0075 1.0158 -0.0572
207 486.6448 0.5771 0.0155 1.0255 0.0723
208 618.4105 0.7326 0.0132 1.0201 0.0846
209 -578.9656 -0.6871 0.0170 1.0250 -0.0903
210 -443.9010 -0.5241 0.0070 1.0176 -0.0441
211 -923.9450 -1.0918 0.0069 1.0042 -0.0908
212 -552.2264 -0.6512 0.0044 1.0128 -0.0434
213 207.9884 0.2465 0.0153 1.0293 0.0307
214 551.6115 0.6508 0.0054 1.0137 0.0477
215 -422.2622 -0.4998 0.0121 1.0231 -0.0552
216 -343.7448 -0.4061 0.0086 1.0208 -0.0379
217 -9.4951 -0.0113 0.0185 1.0335 -0.0015
218 289.0283 0.3414 0.0085 1.0214 0.0317
219 115.6526 0.1378 0.0252 1.0403 0.0221
220 -1002 -1.1842 0.0069 1.0012 -0.0986
221 1240 1.4794 0.0244 1.0078 0.2341
222 100.6099 0.1193 0.0158 1.0305 0.0151
223 77.8125 0.0919 0.0088 1.0233 0.0087
224 668.6121 0.7895 0.0067 1.0122 0.0648
225 -696.6999 -0.8230 0.0073 1.0120 -0.0704
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
181 -0.0039 0.0279 -0.0490 -0.0238 0.0309 0.0484 -0.0138
182 -0.0014 0.0014 -0.0005 0.0009 -0.0044 0.0003 -0.0008
183 -0.0373 0.0211 0.0087 0.0286 0.0207 -0.0133 0.0002
184 -0.0014 -0.0022 0.0043 0.0026 0.0013 -0.0061 0.0011
185 -0.0045 0.0007 -0.0003 0.0034 -0.0033 0.0024 -0.0010
186 -0.0040 -0.0186 -0.0056 0.0076 0.0023 0.0093 -0.0006
187 0.0256 0.0130 0.0403 -0.0239 0.0044 -0.0698 0.0103
188 0.0077 -0.0255 -0.0045 0.0068 -0.0149 0.0077 0.0353
189 -0.0122 0.0133 0.0071 0.0057 -0.0319 -0.0035 -0.0048
190 -0.0041 0.0023 0.0025 0.0029 -0.0060 -0.0012 -0.0008
191 -0.0093 -0.0209 0.0182 0.0079 -0.0419 0.0096 0.0670
192 -0.0210 0.0042 -0.0052 0.0266 0.0195 -0.0066 0.0026
193 0.0027 -0.0004 0.0005 -0.0034 0.0028 0.0009 0.0003
194 -0.0150 -0.0049 0.0614 -0.0216 0.0153 0.0420 -0.0013
195 0.0413 0.0146 -0.0261 -0.0247 -0.0291 -0.0149 0.0006
196 -0.0012 -0.0036 -0.0052 0.0063 -0.0097 -0.0021 -0.0005
197 0.0002 0.0007 -0.0009 0.0000 0.0005 -0.0013 0.0000
198 0.0036 0.0239 0.0112 0.0047 0.0010 -0.0570 0.0066
199 0.0136 0.0032 -0.0096 -0.0093 -0.0098 0.0008 -0.0005
200 -0.0212 0.0079 0.0016 0.0086 0.0180 0.0108 -0.0027
201 -0.0231 0.0027 0.0133 0.0192 0.0146 -0.0128 0.0017
202 -0.0133 0.0139 -0.0095 0.0091 -0.0428 0.0051 -0.0083
203 -0.0272 -0.0659 0.0180 0.0439 -0.0214 0.0432 0.0019
204 -0.0163 -0.0353 0.0065 0.0579 -0.0315 -0.0346 0.0098
205 -0.0145 0.0015 0.0015 0.0197 0.0099 -0.0252 0.0027
206 -0.0397 0.0066 -0.0110 0.0386 0.0205 -0.0044 -0.0015
207 -0.0498 -0.0110 0.0064 0.0427 0.0515 0.0269 0.0018
208 0.0504 -0.0133 0.0093 -0.0497 0.0329 -0.0052 0.0077
209 0.0237 -0.0181 -0.0314 0.0106 -0.0155 -0.0442 0.0050
210 -0.0210 -0.0068 0.0275 0.0178 0.0146 -0.0191 0.0041
211 -0.0557 0.0553 -0.0027 0.0186 0.0539 0.0051 -0.0072
212 -0.0246 -0.0065 0.0201 0.0133 0.0224 -0.0004 0.0006
213 0.0060 0.0068 0.0228 -0.0048 -0.0061 -0.0219 0.0045
214 0.0321 -0.0052 -0.0055 -0.0105 -0.0308 -0.0214 0.0044
215 0.0221 -0.0139 0.0246 -0.0170 -0.0398 -0.0207 0.0018
216 -0.0046 -0.0177 0.0182 -0.0047 0.0124 0.0099 0.0002
217 0.0007 0.0002 -0.0002 -0.0009 0.0002 0.0001 0.0010
218 0.0018 0.0245 0.0013 -0.0096 -0.0005 -0.0005 -0.0012
219 -0.0047 -0.0092 0.0053 0.0005 0.0120 0.0129 0.0002
220 -0.0019 0.0053 0.0508 0.0008 0.0193 -0.0722 0.0112
221 0.0012 0.0486 0.1295 -0.0483 0.1123 -0.0615 -0.1126
222 -0.0057 0.0056 -0.0038 0.0065 0.0084 -0.0027 0.0007
223 0.0019 -0.0029 -0.0017 -0.0005 0.0043 0.0010 0.0007
224 0.0466 -0.0076 0.0203 -0.0251 -0.0366 -0.0390 0.0089
225 -0.0488 -0.0292 0.0031 0.0366 0.0309 0.0356 -0.0041
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
226 -1216 -1.4754 0.0565 1.0422 -0.3609
227 -699.2514 -0.8300 0.0167 1.0215 -0.1080
228 54.0732 0.0649 0.0409 1.0576 0.0134
229 -498.0788 -0.5870 0.0034 1.0129 -0.0342
230 -499.6919 -0.5889 0.0033 1.0127 -0.0339
231 -243.2860 -0.2869 0.0051 1.0185 -0.0206
232 257.8006 0.3073 0.0260 1.0401 0.0502
233 -820.4971 -0.9766 0.0216 1.0228 -0.1451
234 -643.6198 -0.7596 0.0055 1.0117 -0.0567
235 644.8212 0.7621 0.0084 1.0146 0.0702
236 -744.5117 -0.8818 0.0123 1.0157 -0.0985
237 -68.1574 -0.0805 0.0085 1.0230 -0.0075
238 -867.8866 -1.0286 0.0130 1.0124 -0.1182
239 59.1742 0.0697 0.0037 1.0181 0.0042
240 -238.0672 -0.2826 0.0184 1.0322 -0.0387
241 219.3422 0.2586 0.0048 1.0184 0.0180
242 -312.9688 -0.3692 0.0055 1.0180 -0.0274
243 -445.3954 -0.5257 0.0066 1.0171 -0.0428
244 453.4016 0.5418 0.0308 1.0422 0.0966
245 -744.1675 -0.8777 0.0039 1.0072 -0.0551
246 142.0571 0.1674 0.0035 1.0176 0.0100
247 -173.5091 -0.2051 0.0103 1.0243 -0.0209
248 -733.0736 -0.8666 0.0085 1.0122 -0.0803
249 584.2690 0.6918 0.0124 1.0201 0.0774
250 -99.7239 -0.1178 0.0092 1.0236 -0.0114
251 -588.7261 -0.7011 0.0236 1.0317 -0.1091
252 -43.1545 -0.0510 0.0086 1.0232 -0.0047
253 48.6518 0.0575 0.0084 1.0229 0.0053
254 674.9778 0.7995 0.0127 1.0181 0.0905
255 -466.0008 -0.5497 0.0052 1.0153 -0.0396
256 -380.8887 -0.4514 0.0147 1.0265 -0.0551
257 -468.3854 -0.5563 0.0186 1.0291 -0.0767
258 -254.1862 -0.3018 0.0188 1.0326 -0.0418
259 228.0087 0.2705 0.0166 1.0305 0.0351
260 -499.8074 -0.5893 0.0041 1.0135 -0.0378
261 536.4132 0.6368 0.0175 1.0265 0.0849
262 56.0987 0.0667 0.0206 1.0357 0.0097
263 989.5682 1.1758 0.0173 1.0121 0.1561
264 -516.0408 -0.6122 0.0162 1.0256 -0.0786
265 -177.5158 -0.2112 0.0231 1.0377 -0.0325
266 -1437 -1.7102 0.0177 0.9904 -0.2296
267 -1066 -1.2824 0.0410 1.0332 -0.2652
268 854.7948 1.0142 0.0152 1.0150 0.1261
269 -82.9940 -0.0979 0.0062 1.0206 -0.0077
270 -400.3069 -0.4724 0.0064 1.0177 -0.0379
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
226 0.0253 0.0803 0.0038 0.0820 -0.1624 -0.2842 0.0254
227 -0.0407 -0.0055 0.0545 0.0265 0.0350 -0.0240 0.0820
228 0.0043 -0.0003 -0.0015 -0.0021 -0.0041 -0.0021 -0.0117
229 -0.0048 -0.0067 -0.0053 0.0053 0.0099 -0.0040 -0.0002
230 -0.0066 0.0026 0.0070 0.0016 0.0137 -0.0117 0.0009
231 -0.0144 -0.0041 0.0080 0.0103 0.0101 0.0005 0.0002
232 -0.0172 0.0155 0.0339 0.0004 0.0093 0.0009 0.0012
233 0.0233 -0.1139 0.0450 0.0223 -0.0970 -0.0231 0.0079
234 -0.0245 -0.0067 -0.0179 0.0072 0.0281 0.0391 -0.0077
235 0.0212 0.0112 0.0098 -0.0275 0.0462 -0.0098 0.0067
236 -0.0178 -0.0702 0.0158 0.0506 -0.0036 -0.0294 0.0096
237 -0.0016 0.0028 0.0002 0.0004 -0.0039 -0.0003 -0.0008
238 -0.0826 -0.0096 0.0631 0.0769 0.0380 -0.0423 0.0092
239 0.0006 -0.0008 0.0016 -0.0002 -0.0015 0.0003 0.0002
240 0.0242 0.0102 -0.0024 -0.0304 -0.0192 0.0002 -0.0033
241 -0.0009 0.0083 -0.0043 0.0035 -0.0052 -0.0026 -0.0000
242 -0.0125 -0.0095 0.0014 0.0049 0.0131 0.0152 -0.0021
243 -0.0065 -0.0097 0.0180 0.0119 0.0061 -0.0276 0.0051
244 -0.0281 -0.0526 -0.0226 0.0616 -0.0262 0.0200 -0.0489
245 -0.0329 0.0112 0.0127 0.0124 0.0340 0.0028 -0.0021
246 0.0041 0.0006 -0.0036 -0.0008 -0.0055 -0.0004 0.0001
247 -0.0157 0.0040 0.0034 0.0054 0.0132 0.0109 -0.0021
248 0.0067 -0.0589 -0.0032 -0.0009 0.0071 0.0230 -0.0005
249 0.0168 -0.0415 0.0080 0.0286 -0.0433 -0.0408 0.0113
250 -0.0052 0.0009 0.0007 0.0033 -0.0050 0.0030 -0.0013
251 0.0360 0.0347 -0.0397 -0.0645 0.0249 0.0321 0.0531
252 -0.0010 0.0014 0.0010 0.0003 -0.0025 -0.0005 -0.0004
253 -0.0006 0.0021 -0.0005 0.0000 0.0041 -0.0003 0.0003
254 -0.0472 -0.0192 -0.0033 0.0608 0.0520 0.0025 0.0073
255 -0.0122 -0.0237 0.0126 0.0096 0.0123 0.0050 0.0009
256 0.0179 -0.0277 0.0249 -0.0033 -0.0068 -0.0367 0.0083
257 0.0372 0.0360 0.0171 -0.0507 -0.0345 -0.0275 -0.0022
258 0.0250 0.0022 0.0119 -0.0306 -0.0213 -0.0052 -0.0011
259 -0.0121 -0.0158 0.0001 0.0235 0.0124 -0.0051 0.0042
260 -0.0204 -0.0148 0.0039 0.0158 0.0164 0.0082 -0.0008
261 -0.0183 -0.0309 0.0095 0.0599 -0.0317 -0.0398 0.0104
262 -0.0047 -0.0031 -0.0004 0.0075 0.0035 -0.0012 0.0009
263 0.0612 -0.0293 0.1261 -0.0374 -0.0492 -0.1018 0.0268
264 -0.0360 -0.0617 0.0209 0.0391 0.0145 0.0248 0.0015
265 0.0021 -0.0171 0.0223 0.0051 -0.0021 -0.0216 0.0055
266 0.1539 -0.0285 0.0811 -0.1331 -0.0231 -0.1472 0.0252
267 -0.0278 -0.0632 0.0404 0.0234 0.0136 0.0027 -0.2337
268 -0.0145 -0.0212 0.0721 -0.0138 0.0822 0.0175 0.0108
269 -0.0061 -0.0006 0.0013 0.0034 0.0046 0.0032 -0.0005
270 -0.0005 0.0027 0.0173 0.0003 0.0075 -0.0275 0.0040
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
271 1025 1.2134 0.0090 1.0023 0.1155
272 374.8041 0.4467 0.0258 1.0383 0.0726
273 -815.2700 -0.9653 0.0114 1.0125 -0.1036
274 157.3280 0.1856 0.0063 1.0204 0.0148
275 -594.0909 -0.7010 0.0054 1.0128 -0.0516
276 17.5792 0.0207 0.0065 1.0210 0.0017
277 906.9871 1.0743 0.0117 1.0096 0.1169
278 264.3152 0.3120 0.0068 1.0200 0.0258
279 -335.5327 -0.3981 0.0169 1.0296 -0.0522
280 364.4100 0.4349 0.0282 1.0411 0.0741
281 -1332 -1.5945 0.0291 1.0076 -0.2763
282 7.7521 0.009147 0.0064 1.0209 0.0007
283 -723.8636 -0.8578 0.0134 1.0174 -0.1000
284 -196.8353 -0.2342 0.0229 1.0374 -0.0359
285 -253.3283 -0.2994 0.0092 1.0226 -0.0289
286 -944.7845 -1.1226 0.0176 1.0141 -0.1501
287 -670.3834 -0.7924 0.0087 1.0141 -0.0741
288 335.5834 0.3986 0.0191 1.0319 0.0557
289 -1249 -1.4830 0.0143 0.9972 -0.1785
290 -146.3934 -0.1726 0.0044 1.0185 -0.0115
291 -1159 -1.3716 0.0078 0.9953 -0.1219
292 -618.2475 -0.7406 0.0349 1.0428 -0.1407
293 338.8361 0.4024 0.0190 1.0317 0.0560
294 1167 1.3797 0.0070 0.9942 0.1162
295 -1507 -1.7815 0.0035 0.9728 -0.1053
296 354.6217 0.4189 0.0084 1.0204 0.0385
297 804.0285 0.9495 0.0063 1.0077 0.0754
298 106.0794 0.1257 0.0147 1.0293 0.0153
299 -284.0401 -0.3362 0.0123 1.0254 -0.0375
300 -745.0075 -0.8887 0.0262 1.0300 -0.1457
301 -357.9988 -0.4247 0.0165 1.0288 -0.0550
302 -1008 -1.1970 0.0164 1.0104 -0.1544
303 532.9129 0.6313 0.0135 1.0225 0.0738
304 -252.6105 -0.2986 0.0095 1.0229 -0.0293
305 294.5706 0.3500 0.0199 1.0332 0.0499
306 402.3062 0.4766 0.0138 1.0253 0.0563
307 -222.0259 -0.2624 0.0095 1.0232 -0.0257
308 -572.1399 -0.6749 0.0049 1.0127 -0.0471
309 -257.7856 -0.3050 0.0117 1.0251 -0.0332
310 320.2138 0.3861 0.0480 1.0633 0.0867
311 134.2291 0.1586 0.0096 1.0239 0.0156
312 832.2351 0.9821 0.0047 1.0052 0.0676
313 651.7237 0.7710 0.0104 1.0164 0.0789
314 -285.9175 -0.3373 0.0056 1.0185 -0.0254
315 -298.0905 -0.3539 0.0184 1.0315 -0.0484
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
271 -0.0095 -0.0296 0.0764 -0.0006 -0.0122 0.0157 0.0066
272 0.0075 0.0229 -0.0156 -0.0272 0.0062 0.0394 0.0333
273 -0.0565 0.0534 -0.0564 0.0184 0.0532 0.0551 -0.0175
274 0.0117 -0.0003 -0.0033 -0.0059 -0.0091 -0.0055 0.0010
275 -0.0337 -0.0223 0.0112 0.0297 0.0206 0.0075 0.0002
276 -0.0006 -0.0005 0.0002 0.0012 -0.0006 -0.0003 0.0001
277 0.0483 -0.0407 0.0552 0.0040 -0.0613 -0.0887 0.0217
278 0.0026 0.0118 -0.0043 0.0036 -0.0089 -0.0120 0.0012
279 -0.0128 -0.0440 0.0126 0.0155 0.0064 0.0172 0.0010
280 0.0582 -0.0146 0.0104 -0.0417 -0.0332 -0.0261 -0.0339
281 0.1254 -0.2091 -0.0381 -0.0588 -0.0488 0.0343 0.0062
282 0.0000 -0.0003 -0.0002 0.0001 -0.0002 0.0005 -0.0000
283 0.0368 -0.0339 0.0177 -0.0583 0.0169 0.0301 -0.0026
284 0.0139 -0.0109 0.0127 -0.0096 -0.0039 -0.0171 -0.0179
285 -0.0094 -0.0070 -0.0098 0.0169 0.0023 -0.0056 0.0004
286 0.0387 -0.1239 0.0103 0.0127 -0.0254 -0.0269 0.0125
287 -0.0057 0.0141 0.0150 0.0075 -0.0486 -0.0274 -0.0021
288 -0.0319 0.0301 -0.0217 0.0236 0.0071 0.0211 -0.0060
289 -0.0449 0.0017 0.0220 0.0464 0.0246 -0.0530 -0.1294
290 -0.0044 -0.0007 0.0053 0.0032 0.0044 -0.0047 0.0008
291 0.0333 0.0516 0.0322 -0.0507 0.0251 -0.0792 0.0068
292 0.0599 0.0344 0.0358 -0.0526 -0.0102 -0.1036 -0.0554
293 -0.0099 -0.0214 -0.0094 0.0394 -0.0223 -0.0173 0.0047
294 0.0615 0.0068 0.0511 -0.0701 -0.0312 -0.0081 0.0058
295 -0.0385 -0.0351 0.0063 0.0199 0.0472 0.0256 -0.0038
296 0.0015 0.0097 -0.0023 -0.0098 0.0309 0.0086 0.0009
297 0.0484 -0.0253 -0.0133 -0.0094 -0.0502 -0.0254 0.0068
298 0.0038 -0.0058 0.0003 0.0012 -0.0054 -0.0021 0.0126
299 -0.0106 0.0101 0.0224 0.0065 0.0102 -0.0259 0.0038
300 0.0280 -0.0068 -0.1312 -0.0110 -0.0015 0.0531 -0.0167
301 -0.0090 -0.0146 0.0257 0.0114 0.0090 -0.0202 0.0439
302 0.0582 -0.0528 0.1066 -0.0514 -0.0012 -0.0900 0.0214
303 -0.0156 0.0162 0.0087 0.0088 -0.0053 0.0083 -0.0587
304 -0.0190 0.0060 0.0052 0.0036 0.0185 0.0156 -0.0031
305 -0.0207 -0.0058 -0.0085 0.0305 -0.0047 0.0063 0.0320
306 -0.0299 -0.0244 -0.0113 0.0465 -0.0110 0.0166 -0.0001
307 -0.0125 -0.0090 0.0043 0.0040 0.0119 0.0164 -0.0020
308 -0.0237 0.0133 -0.0113 0.0186 0.0196 -0.0058 -0.0020
309 -0.0312 -0.0008 0.0076 0.0229 0.0170 0.0083 -0.0012
310 0.0054 0.0018 -0.0200 -0.0119 0.0010 0.0367 0.0659
311 -0.0035 -0.0052 -0.0077 0.0059 -0.0031 0.0110 -0.0013
312 -0.0007 -0.0274 -0.0111 0.0321 -0.0347 -0.0017 0.0038
313 -0.0268 -0.0299 0.0166 0.0394 0.0456 -0.0053 0.0101
314 -0.0091 0.0126 0.0067 0.0019 0.0119 -0.0100 0.0003
315 -0.0035 0.0057 0.0144 0.0130 -0.0270 -0.0343 0.0029
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
316 -369.9919 -0.4367 0.0068 1.0186 -0.0362
317 33.8482 0.0399 0.0039 1.0183 0.0025
318 22.7376 0.0270 0.0170 1.0319 0.0035
319 -1188 -1.4092 0.0127 0.9987 -0.1598
320 531.3778 0.6307 0.0172 1.0263 0.0833
321 1518 1.8038 0.0137 0.9817 0.2123
322 598.2201 0.7063 0.0066 1.0139 0.0576
323 178.5485 0.2107 0.0062 1.0201 0.0167
324 -1411 -1.6738 0.0114 0.9858 -0.1794
325 2446 2.9263 0.0166 0.9133 0.3798
326 -189.6496 -0.2246 0.0134 1.0274 -0.0261
327 -228.2419 -0.2692 0.0051 1.0186 -0.0193
328 -298.9269 -0.3528 0.0063 1.0191 -0.0281
329 -409.0724 -0.4844 0.0130 1.0244 -0.0557
330 -259.4030 -0.3068 0.0111 1.0244 -0.0325
331 21.8481 0.0259 0.0171 1.0321 0.0034
332 70.2575 0.0833 0.0165 1.0313 0.0108
333 865.3859 1.0232 0.0083 1.0077 0.0935
334 114.7276 0.1355 0.0087 1.0231 0.0127
335 163.4286 0.1930 0.0080 1.0220 0.0173
336 1067 1.2624 0.0089 1.0005 0.1197
337 -197.0277 -0.2335 0.0147 1.0288 -0.0286
338 636.2186 0.7528 0.0109 1.0173 0.0790
339 -511.5163 -0.6045 0.0087 1.0180 -0.0568
340 -1212 -1.4476 0.0255 1.0103 -0.2344
341 -794.6823 -0.9440 0.0178 1.0197 -0.1270
342 -150.9132 -0.1801 0.0283 1.0435 -0.0307
343 -414.0687 -0.5120 0.0949 1.1165 -0.1658
344 -267.9780 -0.3188 0.0222 1.0359 -0.0480
345 503.7369 0.5969 0.0139 1.0235 0.0708
346 240.6730 0.2852 0.0148 1.0285 0.0350
347 595.4753 0.7029 0.0062 1.0135 0.0553
348 -1227 -1.4505 0.0055 0.9898 -0.1083
349 365.3848 0.4323 0.0112 1.0232 0.0460
350 -115.0429 -0.1360 0.0094 1.0238 -0.0133
351 26.0780 0.0308 0.0102 1.0248 0.0031
352 -387.9643 -0.4615 0.0218 1.0339 -0.0689
353 -163.2422 -0.1939 0.0197 1.0342 -0.0275
354 152.4876 0.1802 0.0088 1.0230 0.0170
355 -50.8850 -0.0602 0.0125 1.0273 -0.0068
356 362.5620 0.4285 0.0095 1.0214 0.0419
357 1688 2.0152 0.0214 0.9782 0.2980
358 -289.2570 -0.3411 0.0051 1.0180 -0.0245
359 -589.1093 -0.6967 0.0098 1.0174 -0.0693
360 407.1433 0.4818 0.0115 1.0228 0.0519
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
316 0.0045 0.0123 0.0185 -0.0152 0.0124 -0.0172 0.0018
317 -0.0001 -0.0005 0.0004 0.0011 -0.0012 -0.0006 0.0002
318 -0.0007 -0.0008 0.0008 0.0016 -0.0007 -0.0009 0.0028
319 -0.0246 0.0762 -0.1123 -0.0304 0.0640 0.0950 -0.0295
320 0.0227 0.0008 0.0430 -0.0240 -0.0183 -0.0223 -0.0511
321 0.0960 -0.0733 0.0888 -0.0627 0.0668 -0.0841 0.0369
322 0.0160 0.0161 -0.0072 -0.0279 -0.0072 0.0282 -0.0048
323 0.0133 -0.0052 -0.0010 -0.0082 -0.0096 -0.0013 0.0009
324 -0.0958 0.0778 -0.1151 0.0610 0.0727 0.0634 -0.0251
325 -0.1448 -0.0821 -0.0976 0.1023 0.0124 0.3306 -0.0427
326 -0.0161 0.0028 0.0042 0.0153 -0.0097 -0.0016 -0.0014
327 -0.0001 0.0009 0.0099 -0.0071 0.0085 -0.0017 0.0002
328 -0.0175 -0.0124 0.0122 0.0150 0.0108 0.0008 0.0010
329 -0.0103 0.0038 0.0196 0.0002 0.0186 -0.0094 0.0457
330 -0.0145 0.0096 0.0079 0.0059 -0.0103 0.0036 -0.0031
331 0.0004 -0.0006 -0.0011 -0.0002 0.0012 0.0008 -0.0023
332 0.0094 0.0034 -0.0021 -0.0073 -0.0047 -0.0050 0.0005
333 0.0666 -0.0421 -0.0168 -0.0196 -0.0608 -0.0236 0.0077
334 0.0042 0.0018 -0.0023 -0.0027 0.0066 -0.0032 0.0012
335 0.0098 0.0068 -0.0079 -0.0108 -0.0044 0.0051 -0.0015
336 0.0361 -0.0171 -0.0612 -0.0323 -0.0303 0.0823 -0.0123
337 0.0005 -0.0013 -0.0002 -0.0022 -0.0124 0.0047 0.0190
338 -0.0143 -0.0194 -0.0121 0.0368 0.0361 -0.0127 0.0086
339 -0.0010 0.0044 -0.0182 0.0095 -0.0420 -0.0052 -0.0051
340 -0.0630 -0.0056 -0.1554 0.0589 0.0337 0.1112 -0.1610
341 0.0147 0.0327 -0.0664 -0.0290 0.0164 0.0239 -0.0986
342 0.0012 -0.0074 0.0066 0.0079 -0.0022 -0.0204 0.0204
343 -0.0117 0.0423 -0.0510 -0.0086 0.0162 0.0275 -0.1584
344 -0.0354 0.0046 0.0076 0.0225 0.0228 0.0127 0.0270
345 0.0265 -0.0097 -0.0137 -0.0073 -0.0240 -0.0056 0.0566
346 0.0317 0.0098 0.0000 -0.0288 -0.0134 -0.0129 0.0015
347 0.0038 0.0351 0.0097 -0.0153 -0.0043 -0.0018 -0.0008
348 -0.0648 -0.0037 -0.0500 0.0522 0.0459 0.0435 -0.0115
349 0.0292 -0.0252 -0.0135 -0.0056 -0.0284 -0.0055 0.0028
350 -0.0060 -0.0009 0.0024 0.0043 -0.0061 0.0030 -0.0012
351 0.0014 -0.0010 -0.0000 -0.0006 0.0011 -0.0007 0.0004
352 0.0023 0.0280 0.0052 -0.0328 0.0282 0.0170 0.0370
353 0.0139 -0.0035 0.0072 -0.0180 -0.0130 0.0028 -0.0013
354 0.0011 -0.0029 -0.0029 0.0032 0.0082 -0.0034 0.0019
355 -0.0053 -0.0015 0.0007 0.0058 0.0018 -0.0009 0.0002
356 0.0146 -0.0090 -0.0122 -0.0095 0.0200 0.0059 0.0023
357 -0.0107 -0.0123 0.2069 -0.0694 0.1740 -0.0016 0.0281
358 -0.0175 0.0019 0.0092 0.0101 0.0138 -0.0005 -0.0001
359 -0.0116 -0.0338 0.0170 0.0213 -0.0473 0.0005 -0.0015
360 -0.0322 -0.0181 0.0048 0.0439 -0.0076 0.0077 0.0017
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
361 1308 1.5500 0.0099 0.9899 0.1547
362 -1871 -2.2723 0.0522 0.9943 -0.5334
363 1174 1.3918 0.0109 0.9976 0.1464
364 1437 1.7060 0.0129 0.9858 0.1952
365 -521.6255 -0.6182 0.0142 1.0235 -0.0743
366 146.5069 0.1735 0.0133 1.0277 0.0202
367 536.4550 0.6337 0.0079 1.0167 0.0566
368 501.9212 0.5916 0.0034 1.0128 0.0344
369 365.3881 0.4312 0.0062 1.0180 0.0341
370 -167.4129 -0.1976 0.0073 1.0213 -0.0170
371 175.0922 0.2082 0.0214 1.0359 0.0308
372 -270.5000 -0.3196 0.0089 1.0220 -0.0302
373 -159.8784 -0.1899 0.0197 1.0343 -0.0269
374 47.6570 0.0563 0.0079 1.0224 0.0050
375 -45.9015 -0.0543 0.0104 1.0250 -0.0056
376 -322.8677 -0.3823 0.0130 1.0256 -0.0439
377 1170 1.3820 0.0053 0.9923 0.1008
378 327.9275 0.3871 0.0071 1.0195 0.0328
379 -191.2605 -0.2264 0.0129 1.0269 -0.0259
380 -619.9539 -0.7354 0.0158 1.0227 -0.0930
381 1889 2.2459 0.0113 0.9547 0.2398
382 -336.7246 -0.3979 0.0087 1.0211 -0.0373
383 -487.5295 -0.5753 0.0059 1.0156 -0.0444
384 -141.0611 -0.1665 0.0073 1.0215 -0.0143
385 1114 1.3199 0.0104 0.9999 0.1356
386 -610.5992 -0.7272 0.0237 1.0312 -0.1134
387 366.6471 0.4331 0.0081 1.0200 0.0392
388 1128 1.3344 0.0076 0.9965 0.1168
389 593.1326 0.7008 0.0081 1.0155 0.0631
390 -79.4394 -0.0938 0.0075 1.0220 -0.0082
391 933.5237 1.1073 0.0142 1.0111 0.1330
392 448.4997 0.5303 0.0100 1.0205 0.0533
393 -612.5880 -0.7234 0.0070 1.0139 -0.0605
394 93.0171 0.1101 0.0128 1.0274 0.0125
395 11.3580 0.0134 0.0060 1.0206 0.0010
396 -250.5310 -0.2963 0.0105 1.0239 -0.0305
397 -351.1224 -0.4162 0.0149 1.0273 -0.0512
398 -790.1810 -0.9402 0.0210 1.0232 -0.1377
399 389.6380 0.4597 0.0056 1.0170 0.0345
400 -828.8270 -0.9802 0.0090 1.0096 -0.0933
401 1489 1.7780 0.0236 0.9931 0.2766
402 -51.1173 -0.0605 0.0128 1.0275 -0.0069
403 490.6402 0.5814 0.0142 1.0241 0.0698
404 176.8221 0.2097 0.0166 1.0309 0.0272
405 -144.7470 -0.1722 0.0229 1.0378 -0.0264
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
361 -0.0008 0.0214 0.0549 0.0077 0.0920 -0.0765 0.0246
362 -0.0067 0.2032 -0.4302 -0.0920 0.1194 0.2967 0.1223
363 0.0006 0.0363 0.1094 -0.0249 -0.0076 -0.0414 0.0120
364 -0.0156 -0.0359 -0.0028 0.0521 -0.0368 0.0125 0.1605
365 -0.0174 0.0061 -0.0067 0.0185 0.0100 -0.0153 -0.0563
366 0.0093 -0.0112 -0.0033 0.0028 -0.0125 -0.0075 0.0022
367 -0.0063 -0.0315 -0.0205 0.0261 -0.0209 0.0243 -0.0010
368 0.0048 0.0068 0.0054 -0.0053 -0.0100 0.0040 0.0002
369 0.0259 -0.0031 0.0057 -0.0137 -0.0203 -0.0188 0.0041
370 -0.0012 0.0002 0.0038 0.0002 -0.0114 -0.0011 -0.0011
371 -0.0167 -0.0148 -0.0051 0.0223 0.0132 0.0099 0.0011
372 -0.0106 0.0017 0.0091 0.0087 -0.0162 -0.0035 -0.0014
373 0.0089 -0.0081 -0.0069 -0.0045 -0.0156 0.0034 0.0157
374 0.0036 0.0013 -0.0023 -0.0022 -0.0025 -0.0013 0.0001
375 -0.0004 0.0019 0.0013 -0.0013 -0.0022 0.0006 -0.0006
376 0.0195 -0.0076 0.0207 -0.0292 0.0069 -0.0041 0.0016
377 0.0701 -0.0401 -0.0105 -0.0323 -0.0617 -0.0051 0.0057
378 0.0196 -0.0155 0.0013 -0.0133 -0.0148 0.0072 0.0009
379 -0.0158 -0.0013 0.0022 0.0168 -0.0111 0.0001 -0.0014
380 -0.0006 0.0072 0.0200 0.0204 -0.0003 -0.0781 0.0110
381 0.2214 0.0178 0.0228 -0.1771 -0.1136 -0.1017 0.0184
382 -0.0118 0.0215 0.0151 -0.0003 0.0166 -0.0165 0.0009
383 -0.0158 0.0209 0.0150 0.0033 0.0206 -0.0187 0.0010
384 -0.0108 0.0032 0.0044 0.0043 0.0091 0.0037 -0.0008
385 0.0862 -0.0281 -0.0424 -0.0142 -0.0845 -0.0593 0.0110
386 -0.0468 -0.0768 0.0076 0.0776 -0.0550 0.0133 -0.0005
387 -0.0027 -0.0009 -0.0099 -0.0001 0.0292 0.0146 0.0006
388 0.0528 0.0203 -0.0704 -0.0093 -0.0582 -0.0206 -0.0002
389 0.0125 -0.0201 0.0057 -0.0054 0.0356 -0.0018 0.0074
390 -0.0017 -0.0007 0.0016 0.0017 -0.0054 -0.0003 -0.0005
391 -0.0051 -0.0454 -0.0232 0.0413 -0.0449 0.0179 -0.0997
392 -0.0178 -0.0193 0.0048 0.0271 0.0309 -0.0007 0.0060
393 -0.0113 -0.0036 0.0447 0.0020 0.0190 -0.0308 0.0062
394 0.0000 -0.0001 -0.0045 0.0059 -0.0053 -0.0049 0.0007
395 0.0008 -0.0001 -0.0000 -0.0004 -0.0006 -0.0005 0.0001
396 -0.0138 0.0070 0.0071 0.0064 -0.0106 0.0041 -0.0030
397 -0.0337 -0.0133 0.0045 0.0345 -0.0188 0.0128 -0.0036
398 0.0355 -0.1045 0.0346 -0.0062 -0.0875 0.0054 0.0024
399 0.0127 -0.0054 -0.0210 0.0007 -0.0182 0.0055 -0.0008
400 -0.0850 0.0039 -0.0053 0.0594 0.0508 0.0399 -0.0081
401 -0.0213 -0.1339 0.1118 0.0291 -0.0225 0.0671 0.1744
402 0.0034 0.0014 0.0012 -0.0030 -0.0048 -0.0038 0.0000
403 -0.0221 -0.0228 -0.0139 0.0543 -0.0238 -0.0111 0.0040
404 0.0004 -0.0016 -0.0083 -0.0058 -0.0001 0.0235 -0.0035
405 -0.0015 -0.0209 -0.0023 0.0097 -0.0158 0.0056 -0.0006
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
406 -195.9041 -0.2315 0.0095 1.0234 -0.0227
407 -78.8265 -0.0932 0.0097 1.0242 -0.0092
408 -608.7011 -0.7262 0.0270 1.0348 -0.1210
409 377.8136 0.4461 0.0075 1.0192 0.0387
410 -202.6945 -0.2396 0.0098 1.0236 -0.0239
411 -202.0795 -0.2390 0.0110 1.0249 -0.0252
412 -959.2449 -1.1344 0.0083 1.0042 -0.1039
413 -429.0443 -0.5072 0.0096 1.0205 -0.0500
414 -341.3772 -0.4067 0.0251 1.0381 -0.0652
415 -247.2054 -0.2913 0.0036 1.0168 -0.0175
416 703.0921 0.8327 0.0123 1.0169 0.0929
417 -1703 -2.0314 0.0195 0.9754 -0.2865
418 -163.1994 -0.1925 0.0061 1.0201 -0.0150
419 -376.9749 -0.4445 0.0045 1.0161 -0.0298
420 423.5643 0.4997 0.0057 1.0166 0.0377
421 444.0551 0.5260 0.0136 1.0244 0.0618
422 -391.0959 -0.4621 0.0088 1.0203 -0.0436
423 51.7406 0.0613 0.0144 1.0292 0.0074
424 203.2925 0.2404 0.0105 1.0244 0.0248
425 14.9839 0.0177 0.0124 1.0272 0.0020
426 287.9200 0.3405 0.0105 1.0235 0.0350
427 596.4106 0.7064 0.0129 1.0203 0.0807
428 275.8699 0.3257 0.0074 1.0205 0.0282
429 595.9706 0.7033 0.0055 1.0129 0.0524
430 -162.1483 -0.1923 0.0162 1.0305 -0.0246
431 -797.9310 -0.9436 0.0089 1.0106 -0.0894
432 1207 1.4383 0.0212 1.0061 0.2114
433 87.5537 0.1037 0.0138 1.0285 0.0123
434 221.0290 0.2609 0.0070 1.0206 0.0219
435 2109 2.5030 0.0057 0.9331 0.1896
436 781.4270 0.9248 0.0106 1.0128 0.0956
437 -75.2078 -0.0893 0.0186 1.0335 -0.0123
438 -221.4429 -0.2615 0.0081 1.0218 -0.0237
439 -947.1840 -1.1292 0.0241 1.0207 -0.1776
440 348.6399 0.4116 0.0070 1.0191 0.0346
441 -123.5610 -0.1458 0.0067 1.0210 -0.0120
442 -207.3657 -0.2464 0.0202 1.0345 -0.0354
443 -193.4824 -0.2286 0.0086 1.0224 -0.0212
444 -119.2329 -0.1405 0.0042 1.0184 -0.0091
445 -723.8175 -0.8762 0.0544 1.0611 -0.2102
446 1094 1.3068 0.0271 1.0175 0.2181
447 -365.9584 -0.4329 0.0110 1.0230 -0.0457
448 561.5204 0.6741 0.0392 1.0489 0.1361
449 -468.1724 -0.5518 0.0035 1.0136 -0.0328
450 -687.0289 -0.8113 0.0066 1.0116 -0.0661
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
406 -0.0154 0.0109 0.0063 0.0039 0.0144 0.0039 -0.0015
407 -0.0031 0.0023 0.0020 0.0007 -0.0035 0.0014 -0.0010
408 -0.0150 0.0034 -0.1116 0.0195 0.0135 0.0631 -0.0174
409 0.0081 -0.0066 -0.0016 -0.0051 0.0238 0.0003 0.0037
410 -0.0108 0.0058 0.0014 0.0087 -0.0110 -0.0008 -0.0020
411 -0.0132 0.0055 -0.0045 0.0092 -0.0092 0.0083 -0.0037
412 -0.0376 0.0523 -0.0587 0.0241 0.0366 0.0042 -0.0102
413 -0.0217 0.0112 -0.0336 0.0082 0.0218 0.0339 -0.0088
414 0.0333 0.0215 0.0087 -0.0400 0.0054 -0.0289 0.0397
415 -0.0068 0.0027 0.0003 0.0046 0.0075 -0.0045 -0.0000
416 0.0272 -0.0049 -0.0207 -0.0134 -0.0322 0.0095 -0.0770
417 -0.0715 -0.0516 -0.1175 0.0353 0.0816 0.1759 0.1542
418 -0.0091 0.0030 -0.0038 0.0083 0.0058 -0.0012 -0.0006
419 -0.0152 -0.0003 -0.0057 0.0151 0.0107 -0.0030 -0.0006
420 -0.0089 0.0222 -0.0039 0.0047 -0.0026 0.0046 -0.0018
421 -0.0261 -0.0228 -0.0175 0.0502 -0.0171 0.0063 0.0011
422 0.0168 0.0080 0.0213 -0.0276 0.0098 -0.0182 0.0023
423 0.0020 0.0004 -0.0022 -0.0021 -0.0017 0.0025 -0.0061
424 0.0021 -0.0081 -0.0067 0.0058 0.0096 -0.0024 0.0025
425 -0.0002 0.0005 -0.0000 0.0003 -0.0004 -0.0001 -0.0016
426 0.0046 -0.0057 -0.0074 -0.0089 -0.0039 0.0268 -0.0034
427 0.0187 0.0087 0.0070 -0.0065 -0.0189 -0.0215 0.0689
428 0.0208 -0.0113 -0.0028 -0.0071 -0.0185 -0.0091 0.0027
429 0.0343 0.0092 -0.0108 -0.0159 -0.0298 -0.0234 0.0034
430 -0.0072 0.0042 -0.0022 0.0048 -0.0077 0.0040 0.0152
431 -0.0392 -0.0150 0.0643 0.0322 0.0272 -0.0411 0.0095
432 -0.0449 -0.1138 0.0164 0.0691 -0.0375 0.0855 -0.1321
433 -0.0006 -0.0046 -0.0006 0.0039 -0.0041 0.0009 -0.0091
434 0.0158 -0.0074 0.0053 -0.0066 -0.0136 -0.0113 0.0030
435 0.0799 0.0002 0.0926 -0.0880 -0.0539 -0.0123 0.0113
436 0.0042 -0.0568 -0.0409 0.0420 -0.0443 0.0188 0.0013
437 0.0068 0.0015 0.0033 -0.0054 -0.0010 -0.0101 0.0014
438 -0.0019 -0.0005 0.0091 0.0003 -0.0148 -0.0033 -0.0009
439 0.0113 0.0192 0.0475 0.0277 -0.0084 -0.1595 0.0231
440 0.0218 -0.0172 -0.0096 -0.0075 -0.0205 0.0026 0.0012
441 -0.0037 0.0030 0.0016 0.0037 0.0032 -0.0070 0.0007
442 -0.0164 -0.0238 -0.0054 0.0163 0.0072 0.0230 -0.0022
443 -0.0011 0.0043 0.0001 -0.0040 -0.0107 0.0059 -0.0030
444 -0.0036 0.0003 0.0045 0.0003 0.0050 -0.0005 0.0001
445 0.0211 0.0183 -0.0473 0.0244 -0.0773 -0.0659 0.1631
446 -0.0220 -0.0275 0.1972 -0.0089 0.0004 -0.0394 0.0218
447 -0.0132 0.0218 -0.0345 0.0033 0.0167 0.0183 -0.0073
448 0.0322 0.0153 0.0095 -0.0288 -0.0275 -0.0190 -0.1219
449 -0.0128 0.0029 0.0010 0.0094 0.0137 -0.0083 0.0001
450 -0.0474 -0.0093 -0.0152 0.0309 0.0337 0.0404 -0.0075
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
Hat Diag Cov
Obs Residual RStudent H Ratio DFFITS
451 1364 1.6446 0.0437 1.0205 0.3516
452 431.4733 0.5100 0.0092 1.0200 0.0490
453 -205.1153 -0.2429 0.0136 1.0276 -0.0285
454 -39.2160 -0.0462 0.0053 1.0198 -0.0034
455 -330.7656 -0.3921 0.0154 1.0280 -0.0491
456 -821.1114 -0.9744 0.0158 1.0168 -0.1235
457 476.5952 0.5618 0.0038 1.0137 0.0345
458 325.0201 0.3842 0.0098 1.0223 0.0382
459 -894.3886 -1.0614 0.0155 1.0139 -0.1330
460 -483.8646 -0.5748 0.0190 1.0292 -0.0801
461 -244.9013 -0.2891 0.0073 1.0207 -0.0248
462 426.5026 0.5040 0.0089 1.0198 0.0478
463 -288.2592 -0.3427 0.0208 1.0342 -0.0499
464 -46.5100 -0.0549 0.0060 1.0205 -0.0043
465 -630.5377 -0.7470 0.0132 1.0199 -0.0865
466 -1503 -1.7868 0.0148 0.9837 -0.2191
467 708.9811 0.8366 0.0049 1.0093 0.0590
468 -17.4669 -0.0206 0.0091 1.0238 -0.0020
469 -41.9393 -0.0495 0.0063 1.0208 -0.0039
470 -915.8035 -1.0817 0.0061 1.0037 -0.0846
471 -498.3548 -0.5884 0.0069 1.0164 -0.0491
472 -446.4687 -0.5315 0.0234 1.0346 -0.0823
473 1456 1.7238 0.0076 0.9797 0.1512
474 647.6613 0.7682 0.0155 1.0217 0.0962
475 -1804 -2.1451 0.0122 0.9616 -0.2381
476 -220.6899 -0.2608 0.0094 1.0230 -0.0254
477 -743.5057 -0.8911 0.0354 1.0398 -0.1708
478 -1154 -1.3646 0.0061 0.9938 -0.1069
479 238.2221 0.2823 0.0147 1.0284 0.0345
480 1089 1.2895 0.0107 1.0013 0.1340
481 -228.4774 -0.2698 0.0077 1.0212 -0.0237
482 -1143 -1.3641 0.0248 1.0129 -0.2175
483 -1198 -1.4185 0.0088 0.9944 -0.1334
484 839.0254 0.9948 0.0140 1.0143 0.1183
485 105.7633 0.1256 0.0198 1.0347 0.0178
486 -1833 -2.1831 0.0155 0.9626 -0.2739
487 67.5403 0.0798 0.0086 1.0232 0.0074
488 236.1348 0.2795 0.0126 1.0263 0.0316
489 -584.5019 -0.6973 0.0271 1.0355 -0.1165
490 -638.2786 -0.7570 0.0153 1.0217 -0.0942
491 -209.1926 -0.2481 0.0165 1.0305 -0.0321
492 147.3582 0.1743 0.0107 1.0250 0.0182
493 614.1531 0.7243 0.0044 1.0113 0.0484
494 -2224 -2.6545 0.0146 0.9312 -0.3232
495 1272 1.5042 0.0055 0.9876 0.1121
The REG Procedure
Model: MODEL1
Dependent Variable: water81
Output Statistics
-------------------------------------DFBETAS-------------------------------------
Obs Intercept income water80 educat retired peop81 cpeop
451 -0.0523 -0.0900 0.3144 0.0030 0.0104 -0.0279 0.0326
452 -0.0238 -0.0085 0.0285 0.0273 -0.0051 -0.0054 0.0042
453 -0.0087 -0.0035 -0.0151 0.0129 -0.0155 0.0090 -0.0037
454 -0.0006 0.0021 0.0001 -0.0005 0.0015 -0.0010 -0.0001
455 0.0289 0.0115 -0.0282 -0.0334 0.0027 0.0062 -0.0044
456 -0.0636 0.0252 -0.0520 0.0662 -0.0461 0.0249 -0.0158
457 -0.0021 0.0056 -0.0019 0.0113 -0.0137 -0.0070 0.0016
458 0.0040 0.0049 -0.0036 -0.0139 -0.0009 0.0258 -0.0038
459 0.0145 0.0117 -0.1158 -0.0216 0.0190 0.0675 -0.0198
460 -0.0566 0.0052 0.0152 0.0558 -0.0221 -0.0059 -0.0027
461 0.0028 -0.0041 -0.0004 -0.0020 -0.0191 0.0020 -0.0022
462 0.0168 -0.0106 0.0191 -0.0214 -0.0095 0.0122 0.0009
463 0.0250 0.0176 -0.0052 -0.0384 -0.0186 0.0094 -0.0059
464 -0.0028 -0.0009 0.0022 0.0020 0.0020 -0.0002 0.0001
465 -0.0094 -0.0004 -0.0743 0.0083 0.0154 0.0457 -0.0124
466 -0.0742 0.0877 -0.1762 0.0417 0.0690 0.0928 -0.0341
467 0.0196 -0.0358 0.0119 0.0066 -0.0345 -0.0098 0.0066
468 -0.0009 0.0001 -0.0001 0.0006 -0.0009 0.0007 -0.0003
469 -0.0022 -0.0002 -0.0015 0.0011 0.0020 0.0027 -0.0006
470 -0.0688 0.0160 0.0166 0.0449 0.0477 0.0028 -0.0025
471 0.0228 0.0054 0.0157 -0.0329 0.0099 -0.0167 0.0017
472 0.0033 0.0236 -0.0682 -0.0023 -0.0333 0.0310 -0.0145
473 0.0519 -0.0080 0.0915 -0.0118 -0.0645 -0.1094 0.0254
474 0.0416 0.0697 0.0146 -0.0490 -0.0158 -0.0496 0.0039
475 -0.0347 0.0378 -0.1687 0.0683 0.0242 -0.0086 -0.0151
476 -0.0107 -0.0036 -0.0021 0.0093 -0.0129 0.0094 -0.0032
477 -0.0416 0.0335 -0.1556 0.0286 0.0341 0.1047 -0.0288
478 0.0421 0.0098 -0.0339 -0.0332 0.0067 -0.0390 0.0004
479 -0.0105 -0.0106 -0.0094 0.0264 -0.0117 -0.0042 0.0016
480 -0.0256 -0.0355 
