Greene Chapter 3 Exercise
In this exercise only 15 observations are used and two set of variables are used.
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| Person |
Education |
Wage |
Experience |
Ability |
medu |
fedu |
Sibilings |
| 1 |
13 |
1.82 |
1 |
1 |
12 |
12 |
1 |
| 2 |
15 |
2.14 |
4 |
1.5 |
12 |
12 |
1 |
| 3 |
10 |
1.56 |
1 |
-0.36 |
12 |
12 |
1 |
| 4 |
12 |
1.85 |
1 |
0.26 |
12 |
10 |
4 |
| 5 |
15 |
2.41 |
2 |
0.3 |
12 |
12 |
1 |
| 6 |
15 |
1.83 |
2 |
0.44 |
12 |
16 |
2 |
| 7 |
15 |
1.78 |
3 |
0.91 |
12 |
12 |
1 |
| 8 |
13 |
2.12 |
4 |
0.51 |
12 |
15 |
2 |
| 9 |
13 |
1.95 |
2 |
0.86 |
12 |
12 |
2 |
| 10 |
11 |
2.19 |
5 |
0.26 |
12 |
12 |
2 |
| 11 |
12 |
2.44 |
1 |
1.82 |
16 |
17 |
2 |
| 12 |
13 |
2.41 |
4 |
-1.3 |
13 |
12 |
5 |
| 13 |
12 |
2.07 |
3 |
-0.63 |
12 |
12 |
4 |
| 14 |
12 |
2.2 |
6 |
-0.36 |
10 |
12 |
2 |
| 15 |
12 |
2.12 |
5 |
0.28 |
10 |
12 |
3 |
Analysis
Let X1 equal a constant, education, experience, and ability (the individual’s own characteristics). Let X2 contain the mother’s education, the father’s education, and the number of siblings (the household characteristics). Let y be the log of the hourly wage
a. Compute the least squares regression coefficients in the regression of y on X1. Report the coefficients. b. Compute the least squares regression coefficients in the regression of y on X1 and X2. Report the coefficients.
You can also embed plots, for example:
##
## Call:
## lm(formula = Wage ~ Education + Experience + Ability, data = ch3)
##
## Coefficients:
## (Intercept) Education Experience Ability
## 1.61429 0.01892 0.06602 0.02175
##
## Call:
## lm(formula = Wage ~ Education + Ability + Experience + medu +
## fedu + Sibilings, data = ch3)
##
## Coefficients:
## (Intercept) Education Ability Experience medu fedu
## -0.491974 0.034725 -0.009527 0.121874 0.151657 -0.011383
## Sibilings
## 0.029403
##
## Please cite as:
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
|
(1) |
(2) |
| (Intercept) |
1.614 * |
-0.492 |
|
(0.622) |
(0.924) |
| Education |
0.019 |
0.035 |
|
(0.049) |
(0.040) |
| Experience |
0.066 |
0.122 * |
|
(0.045) |
(0.044) |
| Ability |
0.022 |
-0.010 |
|
(0.098) |
(0.109) |
| medu |
|
0.152 |
|
|
(0.071) |
| fedu |
|
-0.011 |
|
|
(0.041) |
| Sibilings |
|
0.029 |
|
|
(0.064) |
| N |
15 |
15 |
| R2 |
0.183 |
0.602 |
| logLik |
1.051 |
6.451 |
| AIC |
7.898 |
3.098 |
| *** p < 0.001; ** p < 0.01; * p < 0.05. |
Residual Analysis
- Regress each of the three variables in X2 on all the variables in X1 and compute the residuals from each regression. Arrange these new variables in the 15 * 3 matrix X2*. What are the sample means of these three variables? Explain the finding.
- Using (3-26), compute the R2 for the regression of y on X1 and X2. Repeat the computation for the case in which the constant term is omitted from X1. What happens to R2?
- Compute the adjusted R2 for the full regression including the constant term. Interpret your result.
- Referring to the result in part c, regress y on X1 and X2*. How do your results compare to the results of the regression of y on X1 and X2? The comparison you are making is between the least squares coefficients when y is regressed on X1 and M1X2 and when y is regressed on X1 and X2. Derive the result theoretically. (Your numerical results should match the theory, of course.)
resid1<-lm(medu~Education+Experience+Ability,data = ch3)$residuals
resid2<-lm(fedu~Education+Experience+Ability,data = ch3)$residuals
resid3<-lm(Sibilings~Education+Experience+Ability,data = ch3)$residuals
resid1
## 1 2 3 4 5 6
## -1.05221942 0.01216759 -0.71527895 -0.81117002 -0.18653030 -0.24940133
## 7 8 9 10 11 12
## -0.09167214 0.27421779 -0.62055219 0.57274592 2.48826710 2.08705037
## 13 14 15
## 0.32610250 -0.68876015 -1.34496677
X21<-cbind(resid1,resid2,resid3)
X21<-as.data.frame(X21)
dd <- cbind(ch3,X21)
dd<-as.data.frame(dd)
dd
| Person |
Education |
Wage |
Experience |
Ability |
medu |
fedu |
Sibilings |
resid1 |
resid2 |
resid3 |
| 1 |
13 |
1.82 |
1 |
1 |
12 |
12 |
1 |
-1.05 |
-1.27 |
-0.625 |
| 2 |
15 |
2.14 |
4 |
1.5 |
12 |
12 |
1 |
0.0122 |
-1.66 |
-0.0244 |
| 3 |
10 |
1.56 |
1 |
-0.36 |
12 |
12 |
1 |
-0.715 |
-0.0253 |
-2.05 |
| 4 |
12 |
1.85 |
1 |
0.26 |
12 |
10 |
4 |
-0.811 |
-2.61 |
1.64 |
| 5 |
15 |
2.41 |
2 |
0.3 |
12 |
12 |
1 |
-0.187 |
-0.704 |
-1.15 |
| 6 |
15 |
1.83 |
2 |
0.44 |
12 |
16 |
2 |
-0.249 |
3.18 |
-0.0228 |
| 7 |
15 |
1.78 |
3 |
0.91 |
12 |
12 |
1 |
-0.0917 |
-1.19 |
-0.579 |
| 8 |
13 |
2.12 |
4 |
0.51 |
12 |
15 |
2 |
0.274 |
2.24 |
-0.0494 |
| 9 |
13 |
1.95 |
2 |
0.86 |
12 |
12 |
2 |
-0.621 |
-1.12 |
0.255 |
| 10 |
11 |
2.19 |
5 |
0.26 |
12 |
12 |
2 |
0.573 |
-0.455 |
-0.381 |
| 11 |
12 |
2.44 |
1 |
1.82 |
16 |
17 |
2 |
2.49 |
3.06 |
1.08 |
| 12 |
13 |
2.41 |
4 |
-1.3 |
13 |
12 |
5 |
2.09 |
0.778 |
1.28 |
| 13 |
12 |
2.07 |
3 |
-0.63 |
12 |
12 |
4 |
0.326 |
0.207 |
0.833 |
| 14 |
12 |
2.2 |
6 |
-0.36 |
10 |
12 |
2 |
-0.689 |
0.0732 |
-0.889 |
| 15 |
12 |
2.12 |
5 |
0.28 |
10 |
12 |
3 |
-1.34 |
-0.502 |
0.692 |
summary(X21)
## resid1 resid2 resid3
## Min. :-1.3450 Min. :-2.6119 Min. :-2.04748
## 1st Qu.:-0.7020 1st Qu.:-1.1552 1st Qu.:-0.60221
## Median :-0.1865 Median :-0.4551 Median :-0.02439
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.3002 3rd Qu.: 0.4927 3rd Qu.: 0.76255
## Max. : 2.4883 Max. : 3.1768 Max. : 1.63573
##3f
mod3f<- lm(Wage~resid1+resid2+resid3+Education+Experience+Ability ,data=dd)
huxreg(mod3a,mod3b,mod3f)
|
(1) |
(2) |
(3) |
| (Intercept) |
1.614 * |
-0.492 |
1.614 * |
|
(0.622) |
(0.924) |
(0.509) |
| Education |
0.019 |
0.035 |
0.019 |
|
(0.049) |
(0.040) |
(0.040) |
| Experience |
0.066 |
0.122 * |
0.066 |
|
(0.045) |
(0.044) |
(0.037) |
| Ability |
0.022 |
-0.010 |
0.022 |
|
(0.098) |
(0.109) |
(0.080) |
| medu |
|
0.152 |
|
|
|
(0.071) |
|
| fedu |
|
-0.011 |
|
|
|
(0.041) |
|
| Sibilings |
|
0.029 |
|
|
|
(0.064) |
|
| resid1 |
|
|
0.152 |
|
|
|
(0.071) |
| resid2 |
|
|
-0.011 |
|
|
|
(0.041) |
| resid3 |
|
|
0.029 |
|
|
|
(0.064) |
| N |
15 |
15 |
15 |
| R2 |
0.183 |
0.602 |
0.602 |
| logLik |
1.051 |
6.451 |
6.451 |
| AIC |
7.898 |
3.098 |
3.098 |
| *** p < 0.001; ** p < 0.01; * p < 0.05. |