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The Equal Education Opportunity data, table 9.1-9.2, p. 228-229.
data p228; input ACHV FAM PEER SCHOOL ; cards; -0.43148 0.60814 0.03509 0.16607 0.79969 0.79369 0.47924 0.53356 -0.92467 -0.82630 -0.61951 -0.78635 -2.19081 -1.25310 -1.21675 -1.04076 -2.84818 0.17399 -0.18517 0.14229 -0.66233 0.20246 0.12764 0.27311 2.63674 0.24184 -0.09022 0.04967 2.35847 0.59421 0.21750 0.51876 -0.91305 -0.61561 -0.48971 -0.63219 0.59445 0.99391 0.62228 0.93368 1.21073 1.21721 1.00627 1.17381 1.87164 0.41436 0.71103 0.58978 -0.10178 0.83782 0.74281 0.72154 -2.87949 -0.75512 -0.64411 -0.56986 3.92590 -0.37407 -0.13787 -0.21770 4.35084 1.40353 1.14085 1.37147 1.57922 1.64194 1.29229 1.40269 3.95689 -0.31304 -0.07980 -0.21455 1.09275 1.28525 1.22441 1.20428 -0.62389 -1.51938 -1.27565 -1.36598 -0.63654 -0.38224 -0.05353 -0.35560 -2.02659 -0.19186 -0.42605 -0.53718 -1.46692 1.27649 0.81427 0.91967 3.15078 0.52310 0.30720 0.47231 -2.18938 -1.59810 -1.01572 -1.48315 1.91715 0.77914 0.87771 0.76496 -2.71428 -1.04745 -0.77536 -0.91397 -6.59852 -1.63217 -1.47709 -1.71347 0.65101 0.44328 0.60956 0.32833 -0.13772 -0.24972 0.07876 -0.17216 -2.43959 -0.33480 -0.39314 -0.37198 -3.27802 -0.20680 -0.13936 0.05626 -2.48058 -1.99375 -1.69587 -1.87838 1.88639 0.66475 0.79670 0.69865 5.06459 -0.27977 0.10817 -0.26450 1.96335 -0.43990 -0.66022 -0.58490 0.26274 -0.05334 -0.02396 -0.16795 -2.94593 -2.06699 -1.31832 -1.72082 -1.38628 -1.02560 -1.15858 -1.19420 -0.20797 0.45847 0.21555 0.31347 -1.07820 0.93979 0.63454 0.69907 -1.66386 -0.93238 -0.95216 -1.02725 0.58117 -0.35988 -0.30693 -0.46232 1.37447 -0.00518 0.35985 0.02485 -2.82687 -0.18892 -0.07959 0.01704 3.86363 0.87271 0.47644 0.57036 -2.64141 -2.06993 -1.82915 -2.16738 0.05387 0.32143 -0.25961 0.21632 0.50763 -1.42382 -0.77620 -1.07473 0.64347 -0.07852 -0.21347 -0.11750 2.49414 -0.14925 -0.03192 -0.36598 0.61955 0.52666 0.79149 0.71369 0.61745 -1.49102 -1.02073 -1.38103 -1.00743 -0.94757 -1.28991 -1.24799 -0.37469 0.24550 0.83794 0.59596 -2.52824 -0.41630 -0.60312 -0.34951 0.02372 1.38143 1.54542 1.59429 2.51077 1.03806 0.91637 0.97602 -4.22716 -0.88639 -0.47652 -0.77693 1.96847 1.08655 0.65700 0.89401 1.25668 -1.95142 -1.94199 -1.89645 -0.16848 2.83384 2.47398 2.79222 -0.34158 1.86753 1.55229 1.80057 -2.23973 -1.11172 -0.69732 -0.80197 3.62654 1.41958 1.11481 1.24558 0.97034 0.53940 0.16182 0.33477 3.16093 0.22491 0.74800 0.66182 -1.90801 1.48244 1.47079 1.54283 0.64598 2.05425 1.80369 1.90066 -1.75915 1.24058 0.64484 0.87372 ; run;
Table 9.3 and fig. 9.1, p. 229.
symbol v=dot h=.8 c=blue; proc reg data = p228; model achv = fam peer school; plot student.*p.; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: ACHV
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 73.50623 24.50208 5.72 0.0015
Error 66 282.87323 4.28596
Corrected Total 69 356.37946
Root MSE 2.07026 R-Square 0.2063
Dependent Mean 0.01919 Adj R-Sq 0.1702
Coeff Var 10788
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -0.06996 0.25064 -0.28 0.7810
FAM 1 1.10126 1.41056 0.78 0.4378
PEER 1 2.32206 1.48129 1.57 0.1218
SCHOOL 1 -2.28100 2.22045 -1.03 0.3080
The correlations displayed in fig. 9.2, p. 231.
proc corr data=p228; var fam peer school; run;
The CORR Procedure
3 Variables: FAM PEER SCHOOL
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
FAM 70 0.04938 1.08315 3.45683 -2.06993 2.83384
PEER 70 0.04631 0.92480 3.24199 -1.94199 2.47398
SCHOOL 70 0.03191 1.02354 2.23345 -2.16738 2.79222
Pearson Correlation Coefficients, N = 70
Prob > |r| under H0: Rho=0
FAM PEER SCHOOL
FAM 1.00000 0.96008 0.98568
<.0001 <.0001
PEER 0.96008 1.00000 0.98216
<.0001 <.0001
SCHOOL 0.98568 0.98216 1.00000
<.0001 <.0001
Fig. 9.2, p. 231.
Note: Proc insight was not actually invoked here because it has to be terminated manually. If the quit statement is added it will not display the graph.
proc insight data = p228; scatter fam peer school * fam peer school; run;
Import data, table 9.5, p. 233.
data p233; input YEAR IMPORT DOPROD STOCK CONSUM; cards; 49 15.9 149.3 4.2 108.1 50 16.4 161.2 4.1 114.8 51 19 171.5 3.1 123.2 52 19.1 175.5 3.1 126.9 53 18.8 180.8 1.1 132.1 54 20.4 190.7 2.2 137.7 55 22.7 202.1 2.1 146 56 26.5 212.4 5.6 154.1 57 28.1 226.1 5 162.3 58 27.6 231.9 5.1 164.3 59 26.3 239 0.7 167.6 60 31.1 258 5.6 176.8 61 33.3 269.8 3.9 186.6 62 37 288.4 3.1 199.7 63 43.3 304.5 4.6 213.9 64 49 323.4 7 223.8 65 50.3 336.8 1.2 232 66 56.6 353.9 4.5 242.9 ; run;
Creating an index variable.
data p233; set p233; index = _n_; run;
Table 9.6 and fig. 9.3, p. 233.
proc reg data = p233; model import = doprod stock consum; output out = resid student = stdresid; run; quit; goptions reset = all; symbol1 i=join color=blue value=dot h=.8; axis1 label=(angle =90 'Standardized Residuals'); proc gplot data = resid; plot stdresid*index / vaxis=axis1 vref=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: IMPORT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 2576.92075 858.97358 168.45 <.0001
Error 14 71.39037 5.09931
Corrected Total 17 2648.31111
Root MSE 2.25817 R-Square 0.9730
Dependent Mean 30.07778 Adj R-Sq 0.9673
Coeff Var 7.50775
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -19.72511 4.12525 -4.78 0.0003
DOPROD 1 0.03220 0.18688 0.17 0.8656
STOCK 1 0.41420 0.32226 1.29 0.2195
CONSUM 1 0.24275 0.28536 0.85 0.4093
Table 9.7, p. 239 and fig. 9.4, p. 233.
proc reg data = p233; where year LE 59; model import = doprod stock consum; output out=resid student=stdresid; run; quit; goptions reset = all; symbol1 i=join color=blue value=dot h=.8; axis1 label=(angle =90 'Standardized Residuals'); proc gplot data = resid; plot stdresid*index / vaxis=axis1 vref=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: IMPORT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 204.77614 68.25871 285.61 <.0001
Error 7 1.67295 0.23899
Corrected Total 10 206.44909
Root MSE 0.48887 R-Square 0.9919
Dependent Mean 21.89091 Adj R-Sq 0.9884
Coeff Var 2.23321
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -10.12799 1.21216 -8.36 <.0001
DOPROD 1 -0.05140 0.07028 -0.73 0.4883
STOCK 1 0.58695 0.09462 6.20 0.0004
CONSUM 1 0.28685 0.10221 2.81 0.0263
Table 9.8, p. 237.
ods listing close; proc reg data = p233; where year LE 59; model import = doprod; model import = stock; model import = consum; model import = doprod stock; model import = doprod consum; model import = stock consum; model import = doprod stock consum; ods output ParameterEstimates=temp; run; quit; ods output close; ods listing; data temp; set temp; keep model variable estimate; run; proc transpose data = temp out=wide1; by model; var variable estimate; run; proc print data = wide1; var model col1-col4; run;
Obs Model COL1 COL2 COL3 COL4 1 MODEL1 Intercept DOPROD 2 MODEL1 -6.55810 0.14620 3 MODEL2 Intercept STOCK 4 MODEL2 19.61124 0.69081 5 MODEL3 Intercept CONSUM 6 MODEL3 -8.01325 0.21400 7 MODEL4 Intercept DOPROD STOCK 8 MODEL4 -8.44014 0.14531 0.62248 9 MODEL5 Intercept DOPROD CONSUM 10 MODEL5 -8.88431 -0.10875 0.37168 11 MODEL6 Intercept STOCK CONSUM 12 MODEL6 -9.74274 0.59605 0.21230 13 MODEL7 Intercept DOPROD STOCK CONSUM 14 MODEL7 -10.12799 -0.05140 0.58695 0.28685
Advertising data, table 9.9, p. 238. Creating the index variable.
data p238; input S_t A_t P_t E_t A_t_1 P_t_1 ; cards; 20.11371 1.98786 1.0 0.30 2.01722 0.0 15.10439 1.94418 0.0 0.30 1.98786 1.0 18.68375 2.19954 0.8 0.35 1.94418 0.0 16.05173 2.00107 0.0 0.35 2.19954 0.8 21.30101 1.69292 1.3 0.30 2.00107 0.0 17.85004 1.74334 0.3 0.32 1.69292 1.3 18.87558 2.06907 1.0 0.31 1.74334 0.3 21.26599 1.01709 1.0 0.41 2.06907 1.0 20.48473 2.01906 0.9 0.45 1.01709 1.0 20.54032 1.06139 1.0 0.45 2.01906 0.9 26.18441 1.45999 1.5 0.50 1.06139 1.0 21.71606 1.87511 0.0 0.60 1.45999 1.5 28.69595 2.27109 0.8 0.65 1.87511 0.0 25.83720 1.11191 1.0 0.65 2.27109 0.8 29.31987 1.77407 1.2 0.65 1.11191 1.0 24.19041 0.95878 1.0 0.65 1.77407 1.2 26.58966 1.98930 1.0 0.62 0.95878 1.0 22.24466 1.97111 0.0 0.60 1.98930 1.0 24.79944 2.26603 0.7 0.60 1.97111 0.0 21.19105 1.98346 0.1 0.61 2.26603 0.7 26.03441 2.10054 1.0 0.60 1.98346 0.1 27.39304 1.06815 1.0 0.58 2.10054 1.0 ; run;
Creating the index variable.
data p238 ; set p238; index = _n_; run;
Coefficients for equation on bottom of p. 238.
proc reg data = p238; model A_t = P_t P_t_1 A_t_1; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: A_t
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 3.85945 1.28648 213.62 <.0001
Error 18 0.10840 0.00602
Corrected Total 21 3.96786
Root MSE 0.07760 R-Square 0.9727
Dependent Mean 1.75296 Adj R-Sq 0.9681
Coeff Var 4.42706
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 4.63124 0.12937 35.80 <.0001
P_t 1 -0.86953 0.04333 -20.07 <.0001
P_t_1 1 -0.94689 0.04192 -22.59 <.0001
A_t_1 1 -0.86340 0.05024 -17.19 <.0001
Table 9.10 and fig. 9.5-9.6, p. 239-240.
goptions reset = all; symbol1 color=blue value=dot h=.8; proc reg data = p238 ; model S_t = A_t P_t E_t A_t_1 P_t_1 ; plot student.*p.; output out=resid student=stdresid; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: S_t
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 307.57179 61.51436 35.30 <.0001
Error 16 27.87870 1.74242
Corrected Total 21 335.45049
Root MSE 1.32001 R-Square 0.9169
Dependent Mean 22.47579 Adj R-Sq 0.8909
Coeff Var 5.87302
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -14.19366 18.71511 -0.76 0.4592
A_t 1 5.36075 4.02769 1.33 0.2019
P_t 1 8.37232 3.58641 2.33 0.0329
E_t 1 22.52103 2.14235 10.51 <.0001
A_t_1 1 3.85457 3.57772 1.08 0.2973
P_t_1 1 4.12479 3.89511 1.06 0.3053
goptions reset = all; symbol1 i=join color=blue value=dot h=.8; axis1 label=(angle =90 'Standardized Residuals'); axis2 order=(0 to 25 by 5); proc gplot data = resid; plot stdresid*index / haxis=axis2 vaxis=axis1 vref=0; run; quit;
Table 9.11, p. 239.
proc corr data = p238; var A_t P_t E_t A_t_1 P_t_1; run;
The CORR Procedure
5 Variables: A_t P_t E_t A_t_1 P_t_1
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
A_t 22 1.75296 0.43468 38.56506 0.95878 2.27109
P_t 22 0.75455 0.46468 16.60000 0 1.50000
E_t 22 0.49318 0.13947 10.85000 0.30000 0.65000
A_t_1 22 1.79610 0.40987 39.51413 0.95878 2.27109
P_t_1 22 0.70909 0.48786 15.60000 0 1.50000
Pearson Correlation Coefficients, N = 22
Prob > |r| under H0: Rho=0
A_t P_t E_t A_t_1 P_t_1
A_t 1.00000 -0.35695 -0.12852 -0.13974 -0.49599
0.1029 0.5687 0.5351 0.0189
P_t -0.35695 1.00000 0.06259 -0.31647 -0.29636
0.1029 0.7820 0.1513 0.1805
E_t -0.12852 0.06259 1.00000 -0.16643 0.20811
0.5687 0.7820 0.4592 0.3527
A_t_1 -0.13974 -0.31647 -0.16643 1.00000 -0.35776
0.5351 0.1513 0.4592 0.1021
P_t_1 -0.49599 -0.29636 0.20811 -0.35776 1.00000
0.0189 0.1805 0.3527 0.1021
Table 9.12, p. 242.
ods listing close; proc reg data = p228 ; model achv = fam peer school / vif; ods output ParameterEstimates=temp1; run; ods output close; ods listing; data temp1; set temp1; keep dataname variable varianceinflation ; dataname = 'EEO'; run; ods listing close; proc reg data = p233 ; model import = doprod stock consum / vif; ods output ParameterEstimates=temp2; run; ods listing; data temp2; set temp2; keep dataname variable varianceinflation ; dataname = 'Import'; run; ods listing close; proc reg data = p238; model S_t = A_t P_t E_t A_t_1 P_t_1 / vif; ods output ParameterEstimates=temp3; run; ods listing; data temp3; set temp3; keep dataname variable varianceinflation ; dataname = 'Advertising'; run; data mtemp; set temp1 temp2 temp3; run; proc print data= mtemp; var dataname variable varianceinflation; run;
Variance Obs dataname Variable Inflation 1 EEO Intercept 0 2 EEO FAM 37.58064 3 EEO PEER 30.21166 4 EEO SCHOOL 83.15544 5 Imp Intercept 0 6 Imp DOPROD 469.74214 7 Imp STOCK 1.04988 8 Imp CONSUM 469.37134 9 Adv Intercept 0 10 Adv A_t 36.94151 11 Adv P_t 33.47351 12 Adv E_t 1.07596 13 Adv A_t_1 25.91565 14 Adv P_t_1 43.52097
Covariance matrix and correlation matrix on p. 244.
proc corr data = p233 cov; where year <= 59; var doprod stock consum; run;
The CORR Procedure
3 Variables: DOPROD STOCK CONSUM
Covariance Matrix, DF = 10
DOPROD STOCK CONSUM
DOPROD 899.9709091 1.2790000 617.3263636
STOCK 1.2790000 2.7200000 1.2140000
CONSUM 617.3263636 1.2140000 425.7785455
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
DOPROD 11 194.59091 29.99952 2141 149.30000 239.00000
STOCK 11 3.30000 1.64924 36.30000 0.70000 5.60000
CONSUM 11 139.73636 20.63440 1537 108.10000 167.60000
Pearson Correlation Coefficients, N = 11
Prob > |r| under H0: Rho=0
DOPROD STOCK CONSUM
DOPROD 1.00000 0.02585 0.99726
0.9399 <.0001
STOCK 0.02585 1.00000 0.03567
0.9399 0.9171
CONSUM 0.99726 0.03567 1.00000
<.0001 0.9171
The Eigenvalues and Eigenvectors on bottom of p. 246 and principal components in table 9.13, p. 247.
Note: Some of the eigenvectors are the additive inverse of those in the book which is due to the fact that eigenvectors are unique up to a multiple of -1.
ods listing close; proc princomp data = p233 out=temp ; where year <= 59; var doprod stock consum; ods output Eigenvectors=temp1; run; ods listing; proc print data = temp1; run; proc print data = temp; var prin1-prin3; run;
Obs Variable Prin1 Prin2 Prin3 1 DOPROD 0.706330 -.035689 0.706982 2 STOCK 0.043501 0.999029 0.006971 3 CONSUM 0.706544 -.025830 -.707197 Obs Prin1 Prin2 Prin3 1 -2.12589 0.63866 0.020722 2 -1.61893 0.55554 0.071113 3 -1.11517 -0.07298 0.021730 4 -0.89430 -0.08237 -0.010813 5 -0.64421 -1.30669 -0.072582 6 -0.19035 -0.65915 -0.026553 7 0.35962 -0.74367 -0.042781 8 0.97180 1.35406 -0.062863 9 1.55932 0.96405 -0.023574 10 1.76700 1.01522 0.044988 11 1.93110 -1.66266 0.080613
Creating newvar, p. 250.
data p233; set p233; newvar = doprod + consum; run;
Table 9.14 and fig. 9.7-9.8, p. 250-251.
symbol1 c=blue v=dot h=.8; proc reg data = p233; where year <= 59; model import = stock newvar; plot student.*p.; output out=resid student=stdresid; run; quit; symbol1 c=blue v=dot h=.8; symbol1 i=join color=blue value=dot h=.8; axis1 label=(angle =90 'Standardized Residuals'); axis2 order=(0 to 25 by 5); proc gplot data = resid; plot stdresid*index / vaxis=axis1 vref=0; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: IMPORT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 203.85592 101.92796 314.45 <.0001
Error 8 2.59317 0.32415
Corrected Total 10 206.44909
Root MSE 0.56934 R-Square 0.9874
Dependent Mean 21.89091 Adj R-Sq 0.9843
Coeff Var 2.60080
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -9.00680 1.24502 -7.23 <.0001
STOCK 1 0.61164 0.10921 5.60 0.0005
newvar 1 0.08638 0.00356 24.27 <.0001
Beware of all the typos on p. 250, please refer to the Errata web page. The correlation, eigenvalues and eigenvectors of stock and newvar, p. 250.
proc princomp data = p233; where year <= 59; var stock newvar; run;
The PRINCOMP Procedure
Observations 11
Variables 2
Simple Statistics
STOCK newvar
Mean 3.300000000 334.3272727
StD 1.649242250 50.6004168
Correlation Matrix
STOCK newvar
STOCK 1.0000 0.0299
newvar 0.0299 1.0000
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 1.02987334 0.05974667 0.5149 0.5149
2 0.97012666 0.4851 1.0000
Eigenvectors
Prin1 Prin2
STOCK 0.707107 0.707107
newvar 0.707107 -.707107
Table 9.15, p. 253.
proc reg data = p233; where year <= 59; model import = doprod stock ; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: IMPORT
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 202.89371 101.44685 228.27 <.0001
Error 8 3.55538 0.44442
Corrected Total 10 206.44909
Root MSE 0.66665 R-Square 0.9828
Dependent Mean 21.89091 Adj R-Sq 0.9785
Coeff Var 3.04533
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -8.44014 1.43518 -5.88 0.0004
DOPROD 1 0.14531 0.00703 20.67 <.0001
STOCK 1 0.62248 0.12787 4.87 0.0012
The PC coefficients for equations in 9.27, p. 253.
Note: The eigenvectors are unique up to a multiple of -1.
proc princomp data = p238 out = temp; var A_t P_t E_t A_t_1 P_t_1; run;
The PRINCOMP Procedure
Observations 22
Variables 5
Simple Statistics
A_t P_t E_t A_t_1 P_t_1
Mean 1.752957273 0.7545454545 0.4931818182 1.796096818 0.7090909091
StD 0.434678765 0.4646834793 0.1394679128 0.409865806 0.4878613102
Correlation Matrix
A_t P_t E_t A_t_1 P_t_1
A_t 1.0000 -.3570 -.1285 -.1397 -.4960
P_t -.3570 1.0000 0.0626 -.3165 -.2964
E_t -.1285 0.0626 1.0000 -.1664 0.2081
A_t_1 -.1397 -.3165 -.1664 1.0000 -.3578
P_t_1 -.4960 -.2964 0.2081 -.3578 1.0000
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 1.70095474 0.41274783 0.3402 0.3402
2 1.28820691 0.14355527 0.2576 0.5978
3 1.14465164 0.28573629 0.2289 0.8268
4 0.85891534 0.85164396 0.1718 0.9985
5 0.00727138 0.0015 1.0000
Eigenvectors
Prin1 Prin2 Prin3 Prin4 Prin5
A_t -.532445 -.023790 0.667740 0.074417 0.514316
P_t 0.232452 0.824945 -.157793 -.037107 0.489036
E_t 0.389086 -.022080 0.217210 0.894902 -.009710
A_t_1 -.395228 -.259638 -.691911 0.338018 0.428236
P_t_1 0.595714 -.501000 0.057474 -.279247 0.559323
The PC's found by SAS were the additive inverses of those in the book. For a quick fix to get them to be exactly the same just transform them by -1.
proc print data = temp (obs = 10); var prin1-prin5; run; data temp1; set temp; prin1 = -1*prin1; prin3 = -1*prin3; prin5 = -1*prin5; run; proc print data = temp1 (obs = 10); var prin1-prin5; run;
Obs Prin1 Prin2 Prin3 Prin4 Prin5 1 -1.78296 1.04159 -0.48019 -0.63071 -0.03222 2 -0.98031 -1.73963 -0.04034 -1.15494 -0.02050 3 -1.93238 0.71330 0.11408 -0.31791 -0.07203 4 -1.35884 -1.67937 -0.25599 -0.53532 0.03520 5 -1.25604 1.60055 -1.00787 -0.71848 -0.08235 6 0.12229 -1.32047 0.11365 -1.49990 0.09198 7 -1.22412 0.90098 0.15783 -0.95023 0.12096 8 0.88410 0.01753 -1.76986 -0.62071 0.01215 9 0.73275 0.44523 1.64148 -1.05210 -0.00946 10 0.86754 0.14315 -1.56687 -0.34047 -0.10512 Obs Prin1 Prin2 Prin3 Prin4 Prin5 1 1.78296 1.04159 0.48019 -0.63071 0.03222 2 0.98031 -1.73963 0.04034 -1.15494 0.02050 3 1.93238 0.71330 -0.11408 -0.31791 0.07203 4 1.35884 -1.67937 0.25599 -0.53532 -0.03520 5 1.25604 1.60055 1.00787 -0.71848 0.08235 6 -0.12229 -1.32047 -0.11365 -1.49990 -0.09198 7 1.22412 0.90098 -0.15783 -0.95023 -0.12096 8 -0.88410 0.01753 1.76986 -0.62071 -0.01215 9 -0.73275 0.44523 -1.64148 -1.05210 0.00946 10 -0.86754 0.14315 1.56687 -0.34047 0.10512
Table 9.16, p. 256. The estimated coefficients in the table 9.16 correspond to the standardized estimates in the output.
proc reg data = p238; model S_t = A_t P_t E_t A_t_1 P_t_1/stb; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: S_t
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 307.57179 61.51436 35.30 <.0001
Error 16 27.87870 1.74242
Corrected Total 21 335.45049
Root MSE 1.32001 R-Square 0.9169
Dependent Mean 22.47579 Adj R-Sq 0.8909
Coeff Var 5.87302
Parameter Estimates
Parameter Standard Standardized
Variable DF Estimate Error t Value Pr > |t| Estimate
Intercept 1 -14.19366 18.71511 -0.76 0.4592 0
A_t 1 5.36075 4.02769 1.33 0.2019 0.58303
P_t 1 8.37232 3.58641 2.33 0.0329 0.97342
E_t 1 22.52103 2.14235 10.51 <.0001 0.78588
A_t_1 1 3.85457 3.57772 1.08 0.2973 0.39529
P_t_1 1 4.12479 3.89511 1.06 0.3053 0.50349
Creating the standardized variable for S_t to be used in regression p. 257.
proc sql; create table tempstd as select *, (S_t - mean(S_t))/std(S_t) as zs_t from temp1; quit;
Table 9.17, p. 257.
Note: The regression model has no intercept (the noint option in the model statement) because all the variables have been standardized.
proc reg data = tempstd; model zs_t = prin1-prin5/noint; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: zs_t
NOTE: No intercept in model. R-Square is redefined
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 19.25473 3.85095 37.51 <.0001
Error 17 1.74527 0.10266
Uncorrected Total 22 21.00000
Root MSE 0.32041 R-Square 0.9169
Dependent Mean -3.1288E-16 Adj R-Sq 0.8924
Coeff Var -1.02407E17
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Prin1 1 -0.36533 0.05361 -6.81 <.0001
Prin2 1 0.41691 0.06160 6.77 <.0001
Prin3 1 -0.16185 0.06535 -2.48 0.0241
Prin4 1 0.70357 0.07544 9.33 <.0001
Prin5 1 -1.21916 0.81995 -1.49 0.1554
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