Stat Computing > Stata > Textbook Examples > Applied Linear Statistical Models, by Neter, Kutner, Nachtsheim, and Wasserman
Stata Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 19: Two-factor Analysis of Variance-Equal Sample Sizes
Inputting the Castle Bakery data, table 19.7, p. 818.
input sales height width store 47 1 1 1 43 1 1 2 46 1 2 1 40 1 2 2 62 2 1 1 68 2 1 2 67 2 2 1 71 2 2 2 41 3 1 1 39 3 1 2 42 3 2 1 46 3 2 2 end
Table 19.7, p. 818.
table height width, contents(sum sales mean sales) row col
-------------------------------
| width
height | 1 2 Total
----------+--------------------
1 | 90 86 176
| 45 43 44
|
2 | 130 138 268
| 65 69 67
|
3 | 80 88 168
| 40 44 42
|
Total | 300 312 612
| 50 52 51
-------------------------------
Fig. 19.6, p. 820. This figure uses anovaplot, a user written program. You can download it by typing findit anovaplot (see How can I used the findit command to search for programs and get additional help? for more information about using findit).
anova sales height width height*width anovaplot, scatter(ms(i)) xlabel(1 "A1" 2 "A2" 3 "A3")
Table 19.9, p. 820-824.
anova sales height width height*width
Number of obs = 12 R-squared = 0.9622
Root MSE = 3.21455 Adj R-squared = 0.9308
Source | Partial SS df MS F Prob > F
-------------+----------------------------------------------------
Model | 1580 5 316 30.58 0.0003
|
height | 1544 2 772 74.71 0.0001
width | 12 1 12 1.16 0.3226
height*width | 24 2 12 1.16 0.3747
|
Residual | 62 6 10.3333333
-------------+----------------------------------------------------
Total | 1642 11 149.272727
Figure 19.8, p. 828.
anova sales height width height*width predict yhat predict r, residuals twoway scatter r yhat, m(x) msize(huge) qnorm r, m(x) msize(huge)
| (a) | (b) |
 |
 |
F tests of the interaction and main effects, p. 830-831.
Note the F tests are included in the standard output and have been italicized for illustration.
anova sales height width height*width
Number of obs = 12 R-squared = 0.9622
Root MSE = 3.21455 Adj R-squared = 0.9308
Source | Partial SS df MS F Prob > F
-------------+----------------------------------------------------
Model | 1580 5 316 30.58 0.0003
|
height | 1544 2 772 74.71 0.0001
width | 12 1 12 1.16 0.3226
height*width | 24 2 12 1.16 0.3747
|
Residual | 62 6 10.3333333
-------------+----------------------------------------------------
Total | 1642 11 149.272727
Creating the dummy and interaction variables for the Regression model of the Bakery data, p. 833.
gen x1 = 0 recode x1 0 = 1 if height == 1 recode x1 0 = -1 if height == 3 gen x2 = 0 recode x2 0 = 1 if height == 2 recode x2 0 = -1 if height == 3 gen x3 = -1 recode x3 -1 = 1 if width == 1 gen x1x3 = x1*x3 gen x2x3 = x2*x3 list height width x1 x2 x3 x1x3 x2x3
+---------------------------------------------+
| height width x1 x2 x3 x1x3 x2x3 |
|---------------------------------------------|
1. | 1 1 1 0 1 1 0 |
2. | 1 1 1 0 1 1 0 |
3. | 1 2 1 0 -1 -1 0 |
4. | 1 2 1 0 -1 -1 0 |
5. | 2 1 0 1 1 0 1 |
|---------------------------------------------|
6. | 2 1 0 1 1 0 1 |
7. | 2 2 0 1 -1 0 -1 |
8. | 2 2 0 1 -1 0 -1 |
9. | 3 1 -1 -1 1 -1 -1 |
10. | 3 1 -1 -1 1 -1 -1 |
|---------------------------------------------|
11. | 3 2 -1 -1 -1 1 1 |
12. | 3 2 -1 -1 -1 1 1 |
+---------------------------------------------+
Table 19.10a, p. 836.
list height width store sales x1 x2 x3 x1x3 x2x3
+-------------------------------------------------------------+
| height width store sales x1 x2 x3 x1x3 x2x3 |
|-------------------------------------------------------------|
1. | 1 1 1 47 1 0 1 1 0 |
2. | 1 1 2 43 1 0 1 1 0 |
3. | 1 2 1 46 1 0 -1 -1 0 |
4. | 1 2 2 40 1 0 -1 -1 0 |
5. | 2 1 1 62 0 1 1 0 1 |
|-------------------------------------------------------------|
6. | 2 1 2 68 0 1 1 0 1 |
7. | 2 2 1 67 0 1 -1 0 -1 |
8. | 2 2 2 71 0 1 -1 0 -1 |
9. | 3 1 1 41 -1 0 1 -1 0 |
10. | 3 1 2 39 -1 0 1 -1 0 |
|-------------------------------------------------------------|
11. | 3 2 1 42 -1 0 -1 1 0 |
12. | 3 2 2 46 -1 0 -1 1 0 |
+-------------------------------------------------------------+
Table 19.10c, p. 836.
anova sales x1 x2 x3 x1x3 x2x3, seq cont( x1 x2 x3 x1x3 x2x3)
Number of obs = 12 R-squared = 0.9622
Root MSE = 3.21455 Adj R-squared = 0.9308
Source | Seq. SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 1580 5 316 30.58 0.0003
|
x1 | 8 1 8 0.77 0.4128
x2 | 1536 1 1536 148.65 0.0000
x3 | 12 1 12 1.16 0.3226
x1x3 | 18 1 18 1.74 0.2350
x2x3 | 6 1 6 0.58 0.4749
|
Residual | 62 6 10.3333333
-----------+----------------------------------------------------
Total | 1642 11 149.272727
Pooling sums of squares in the Bakery Sales example, p. 837.
anova sales height width
Number of obs = 12 R-squared = 0.9476
Root MSE = 3.27872 Adj R-squared = 0.9280
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 1556 3 518.666667 48.25 0.0000
|
height | 1544 2 772 71.81 0.0000
width | 12 1 12 1.12 0.3216
|
Residual | 86 8 10.75
-----------+----------------------------------------------------
Total | 1642 11 149.272727
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