Problem 4 (25 Points)
A professor of Economics wants to evaluate whether he has any gender bias in grading the students, as well as whether students perform worse when taking online courses. After collecting data from the last two years, he obtained the following outcome when regressing the grade on two dummies: gender (male=1, female=0), online (online=1, in-person=0).
grade = 90 - 1.98 * gender - 13.45 * online
(3.60)
(2.56)
(3.60)
n = 178, R-squared = 0.07
a) Based on the rule of thumb, how do you interpret this outcome? (5 points)
b) Someone told this professor that he needs to consider the efforts made by his students. Then, this professor decided to run another regression including the grades from the Problem Sets and the Midterm. After adding these new variables, he found the following:
Source Ss MS Number of obs F4,173 4 10015.5729 Prob > F 173 84.6059646 R-squared Adj R-squared 177 309.034597 Root MSE
178 118.38 .0000 .7324 .7262 9.1982
Model Residual
40062.2917 14636.8319
Total
54699.1236
grade
Coef. Std.Err. t P>|t| [95% Conf.Interval]
gender online ps mdexam
-1.241734 -1.25488 2457987 .6722195 8.581656
1.387365 2.055563 .0234776 .0415696 4.429438
-0.90 .372 -0.61 .542 10.47 0.000 16.17 0.000 1.94 .054
-3.980076 -5.312092 .1994593 .5901706 -.1610416
1.496608 2.802332 .292138 7542684 17.32435
Interpret this new outcome [gender, online, problem sets (ps), and mdexam (midterm exam grade)], stressing the differences that you have found in letter a. (10 points)
c) He showed his outcome to a gender specialist, and this person said: "You should know that the pandemic has affected many more women than men, so your outcome might be influenced by the grades obtained by women attending in person without any home obligations. Their performance might have offset the bad outcomes of those suffering while doing their home tasks while attending your classes. Everyone knows that women perform much better than men in general, so it is important to consider this factor in your analysis."
The professor ran another regression creating other dummies for gender and online, and he found the following outcome.
