Program 11.1
- Figures 11.1, 11.2, and 11.3
- Sample averages by treatment level
clear
**Figure 11.1**
*create the dataset*
input A Y
1 200
1 150
1 220
1 110
1 50
1 180
1 90
1 170
0 170
0 30
0 70
0 110
0 80
0 50
0 10
0 20
end
*Save the data*
qui save ./data/fig1, replace
*Build the scatterplot*
scatter Y A, ylab(0(50)250) xlab(0 1) xscale(range(-0.5 1.5))
qui gr export figs/stata-fig-11-1.png, replace
*Output the mean values for Y in each level of A*
bysort A: sum Y
A Y
1. 1 200
2. 1 150
3. 1 220
4. 1 110
5. 1 50
6. 1 180
7. 1 90
8. 1 170
9. 0 170
10. 0 30
11. 0 70
12. 0 110
13. 0 80
14. 0 50
15. 0 10
16. 0 20
17. end
--------------------------------------------------------------------------------------
-> A = 0
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 8 67.5 53.11712 10 170
--------------------------------------------------------------------------------------
-> A = 1
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 8 146.25 58.2942 50 220
*Clear the workspace to be able to use a new dataset*
clear
**Figure 11.2**
input A Y
1 110
1 80
1 50
1 40
2 170
2 30
2 70
2 50
3 110
3 50
3 180
3 130
4 200
4 150
4 220
4 210
end
qui save ./data/fig2, replace
scatter Y A, ylab(0(50)250) xlab(0(1)4) xscale(range(0 4.5))
qui gr export figs/stata-fig-11-2.png, replace
bysort A: sum Y
A Y
1. 1 110
2. 1 80
3. 1 50
4. 1 40
5. 2 170
6. 2 30
7. 2 70
8. 2 50
9. 3 110
10. 3 50
11. 3 180
12. 3 130
13. 4 200
14. 4 150
15. 4 220
16. 4 210
17. end
--------------------------------------------------------------------------------------
-> A = 1
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 4 70 31.62278 40 110
--------------------------------------------------------------------------------------
-> A = 2
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 4 80 62.18253 30 170
--------------------------------------------------------------------------------------
-> A = 3
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 4 117.5 53.77422 50 180
--------------------------------------------------------------------------------------
-> A = 4
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
Y | 4 195 31.09126 150 220
clear
**Figure 11.3**
input A Y
3 21
11 54
17 33
23 101
29 85
37 65
41 157
53 120
67 111
79 200
83 140
97 220
60 230
71 217
15 11
45 190
end
qui save ./data/fig3, replace
scatter Y A, ylab(0(50)250) xlab(0(10)100) xscale(range(0 100))
qui gr export figs/stata-fig-11-3.png, replace
A Y
1. 3 21
2. 11 54
3. 17 33
4. 23 101
5. 29 85
6. 37 65
7. 41 157
8. 53 120
9. 67 111
10. 79 200
11. 83 140
12. 97 220
13. 60 230
14. 71 217
15. 15 11
16. 45 190
17. end
Program 11.2
- 2-parameter linear model
- Creates Figure 11.4, parameter estimates with 95% confidence intervals from Section 11.2, and parameter estimates with 95% confidence intervals from Section 11.3
**Section 11.2: parametric estimators**
*Reload data
use ./data/fig3, clear
*Plot the data*
scatter Y A, ylab(0(50)250) xlab(0(10)100) xscale(range(0 100))
*Fit the regression model*
regress Y A, noheader cformat(%5.2f)
*Output the estimated mean Y value when A = 90*
lincom _b[_cons] + 90*_b[A]
*Plot the data with the regression line: Fig 11.4*
scatter Y A, ylab(0(50)250) xlab(0(10)100) xscale(range(0 100)) || lfit Y A
qui gr export figs/stata-fig-11-4.png, replace
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
A | 2.14 0.40 5.35 0.000 1.28 2.99
_cons | 24.55 21.33 1.15 0.269 -21.20 70.29
------------------------------------------------------------------------------
( 1) 90*A + _cons = 0
------------------------------------------------------------------------------
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 216.89 20.8614 10.40 0.000 172.1468 261.6333
------------------------------------------------------------------------------
**Section 11.3: non-parametric estimation*
* Reload the data
use ./data/fig1, clear
*Fit the regression model*
regress Y A, noheader cformat(%5.2f)
*E[Y|A=1]*
di 67.50 + 78.75
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
A | 78.75 27.88 2.82 0.014 18.95 138.55
_cons | 67.50 19.72 3.42 0.004 25.21 109.79
------------------------------------------------------------------------------
146.25
Program 11.3
- 3-parameter linear model
- Creates Figure 11.5 and Parameter estimates for Section 11.4
* Reload the data
use ./data/fig3, clear
*Create the product term*
gen Asq = A*A
*Fit the regression model*
regress Y A Asq, noheader cformat(%5.2f)
*Output the estimated mean Y value when A = 90*
lincom _b[_cons] + 90*_b[A] + 90*90*_b[Asq]
*Plot the data with the regression line: Fig 11.5*
scatter Y A, ylab(0(50)250) xlab(0(10)100) xscale(range(0 100)) || qfit Y A
qui gr export figs/stata-fig-11-5.png, replace
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
A | 4.11 1.53 2.68 0.019 0.80 7.41
Asq | -0.02 0.02 -1.33 0.206 -0.05 0.01
_cons | -7.41 31.75 -0.23 0.819 -75.99 61.18
------------------------------------------------------------------------------
( 1) 90*A + 8100*Asq + _cons = 0
------------------------------------------------------------------------------
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 197.1269 25.16157 7.83 0.000 142.7687 251.4852
------------------------------------------------------------------------------
