# HW 3 solutions

```Econ 526
Econometrics Problem Set #3
1. Add variable labels to beauty course_eval intro nnenglish and then describe and
summarize your data. Below, report the mean of course_eval and the mean of
beauty. Interpret these numbers. (10 points)
storage
variable name
type
display
value
format
label
variable label
----------------------------------------------------------------------------------minority
float
%9.0g
Minority
age
float
%9.0g
Professor's age
female
float
%9.0g
female = 1
onecredit
byte
%8.0g
Equal 1 if a one-credit course
beauty
float
%9.0g
Standardized ranking of Beauty
course_eval
float
%9.0g
Teaching Evaluation 1-poor 5-great
intro
float
%9.0g
Introductory Course
nnenglish
float
%9.0g
Non-Native English Speaker
. summarize *;
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------minority |
463
.1382289
.3455134
0
1
age |
463
48.36501
9.802742
29
73
female |
463
.4211663
.4942802
0
1
onecredit |
463
.0583153
.2345922
0
1
beauty |
463
4.75e-08
.7886477
-1.450494
1.970023
-------------+-------------------------------------------------------course_eval |
463
3.998272
.5548656
2.1
5
intro |
463
.3390929
.4739135
0
1
1
nnenglish |
463
.0604752
.2386229
0
1
Mean Beauty = 0. Mean Course evaluation = 3.998 out of a five point scale.
Course evaluations are skewed to the right.
2. Create a histogram of beauty and impose the normal distribution on this graph.
Do the same for course evaluations. Print and attach these graphs. Interpret these
graphs. Do the data violate any regression assumptions? (15 points)
2
Beauty is skewed to the left—which means that there are more people with below
average beauty. However Course Evaluations are skewed to the right. Both
distributions also have multiple modes. Given that both data series are
skewed, the assumption of normally distributed errors is likely violated.
3. Create a scatterplot of Course_eval and beauty. Insert a regression line in this
scatterplot. Print off and attach your graph (be sure to have a title). Report the
correlation between course_eval and beauty below. (15 points).
Beauty and Course_eval have a small positive correlation of .189. You can see that
there is a positive slope on the graph.
4. Regress course_eval on beauty. Write the equation for the regression line below.
Explain why the intercept is equal to the sample mean of course_eval (hint: see
your answer to question 1 above) Is beauty significantly different from zero? (10
points).
Course_ eval = 3.998 +.133Beauty
Beauty is significantly different from zero. The t-statistic tests the null hypothesis
that the coefficient on beauty equals zero, and 4.13 > 1.96, so we reject the null.
3
5. Professor Watson has average beauty while Professor Holmes beauty is one
standard deviation above average. Predict Professor Watson’s and Professor
Holmes’ course evaluations. (10 points)
Watson’s course evaluations: Course_ eval = 3.998 + .133 ´ 0 = 3.998
Holmes’ course evaluations: Course_ eval = 3.998 +.133´.789 = 4.102
6. Now regress Course_eval on beauty, intro, onecredit, female, minority, and
nnenglish. Use robust standard errors. How will the standard errors change now
that you have relaxed the homoscedasticity assumption? How does the
coefficient on beauty change compared to question 3? Is beauty significantly
different from zero? (15 points)
The standard errors will be larger than in the previous regression because of
correcting for heteroskedasticity. The table below shows the
coefficients from the regression for Question 4, 6, and 8. The
coefficient on beauty actually increases once you control for other
characteristics. It is significantly different from zero in this regression
as well.
VARIABLES
Standardized ranking of Beauty
(1)
(2)
Question 4 Question 6
0.133***
[0.032]
0.104*
[0.040]
0.244***
[0.048]
3.998***
[0.025]
-0.240*
[0.094]
0.363
[0.205]
-0.148
[0.109]
-0.021
[0.094]
3.932***
[0.049]
0.027
[0.094]
0.708***
[0.104]
-0.407**
[0.127]
0.039
[0.069]
4.049***
[0.042]
463
0.036
463
0.155
195
0.071
268
0.223
Minority
Equal 1 if a one-credit course
Non-Native English Speaker
Introductory Course
Observations
R-squared
Standard errors in brackets
*** p<0.001, ** p<0.01, * p<0.05
(4)
Male
0.166***
[0.032]
-0.173***
[0.049]
-0.167*
[0.067]
0.635***
[0.108]
-0.244**
[0.094]
0.011
[0.056]
4.068***
[0.037]
female = 1
Constant
(3)
Female
4
7. Professor Smith is a black man with average beauty and a nonnative English
speaker. He teaches a three credit upper-division course. Predict Professor
Smith’s course evaluations. (10 points)
Course _ eval = 4.068 + .166Beauty -.173Female
-.166Minority + .635onecredit -.244Nnenglish + .011int ro
Course _ eval = 4.068 -.166 -.224 = 3.658
8. Run the same regression in #6 separately for male and female professors.
Compare and contrast the coefficients in each regression. Predict the effect of one
standard deviation increase in beauty on course evaluations for a white professor
who is a native speaker of English teaching an upper level course for both men
and women. Explain your result. (15 points)
Examining the table above, you see that the effect of beauty is more than twice as
large for men compared to women. Also, women are penalized in
teaching evaluation more for being minorities. Men get over twice as
much ‘return’ on teaching one credit courses compared to women.
However, they are penalized almost three times as much for being
non-native English speakers.
As shown by the predictions below, women of above average beauty get less of a
return on that compared to men.
Course _ evalF = 3.932 + .104 Beauty - .240Minority
+.363onecredit - .148 Nnenglish - .021int ro
Course _ eval M = 4.049 + .244 Beauty - .027Minority
+.708onecredit - .407Nnenglish - .039 int ro
Course _ evalF = 3.932 + .104 ´ .789 = 4.01
Course _ eval M = 4.049 + .244 ´ .789 = 4.24
5
Do-file commands
******* Question 1 *********;
label var beauty "Standardized ranking of Beauty";
label var course_eval "Teaching Evaluation 1-poor 5-great";
label var intro "Introductory Course";
label var nnenglish "Non-Native English Speaker";
describe *;
summarize *;
******* Question 2 *********;
histogram beauty, normal;
histogram course_eval, normal;
******* Question 3 *********;
twoway scatter course_eval beauty || lfit course_eval beauty;
corr beauty course_eval;
******* Question 4 *********;
regress course_eval beauty;
outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05)
bracket ct(1) replace;
******* Question 6 *********;
regress course_eval beauty female minority onecredit nnenglish intro, robust;
outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05)
bracket ct(1) append;
******* Question 8 *********;
regress course_eval beauty minority onecredit nnenglish intro if female==1, robust;
outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05)
bracket ct(1) append;
regress course_eval beauty minority onecredit nnenglish intro if female==0, robust;
outreg2 using problemset3sol.xls, bd(3) td(3) label alpha(.001, .01, .05)
bracket ct(1) append;
6
```