problem solving

Assignment 2
Introduction to Econometrics
STATA OUTPUT – For a

The sample mean for beauty ratings is -0.0109287, as shown from the output.
STATA OUTPUT – Q b

The regression output predicts course evaluation using beauty, with beauty being the independent variable while the course evaluation is the dependent variable. From the output the null hypothesis from the F-test is that the R-squared is 0, but the F-test value is 0.0085 which is less than 0.05, therefore we reject the null hypothesis with 95% level of confidence.
The R-squared, 0.0197 shows that the model explains only 1.97% of the variation in course evaluation is explained by the model, because the model does not explain 98.03%, we can conclude that it is a worse model.
The t-test for beauty has a p-value of 0.009, which is less than 0.05 therefore we can reject the null hypothesis at 95% confidence level and conclude that beauty has a significant effect on the course evaluation.
The coefficients of the variables are 0.0983013 for beauty and 4.02936 for constant. This explains that for every unit increase in the beauty there is a significant increase in course evaluation by 0.0983013. The correlation between beauty and course evaluation is positive therefore any change in beauty will influence an increment on course evaluation. The coefficient for the constant at 4.02936 is the value of course evaluation when beauty is zero.
The coefficient on beauty is significant at 5% level since it has a p-value that is less than 0.

05.
c.
STATA OUTPUT –Q c

We run the regression with option 1 of onecredit omitted, since we want an indicative variable with classes not single credit represented by 0.
The F-test is below 0.05 indicating that the model is statistically significant. The R-squared is 0.0629 which explains that 6.29% of the variance of course evaluation can be accounted for by the model. The t-tests for classes not single credit is -4.83 with a p-value of 0.000 which is below 0.05 and hence statistically significant.
The coefficient for classes not single credit is -0.5567074 which shows that for every unit increase in there will be a decrease in course evaluation by 0.5567074. When the classes not single credit is zero then the value of course evaluation will be 4.55
d.
STATA OUTPUT-Q d

The F-test from the output is 0.0001 which is below 0.05 hence we can reject the null hypothesis. R-squared is 0.0608, which shows that our model explains 6.08% of the course evaluation.
From the t-test we can see that the coefficient beauty has a p-value of 0.190 which is above 0.05 and therefore it is not statistically significant. The coefficient for beauty2 is statistically significant t a p-value of 0.002 which is below 0.05. In additional the coefficient for beauty3 is also statistically significant with a p-value of 0.000 which is below 0.05.
The coefficient for beauty2 and beauty3 are therefore significant at 5% level.
e. STATA OUTPUT
00
f)
STATA OUTPUT Q-f

From the regression output we can see that the F-test is statistically significant since it is below 0.05 and therefore the model is statistically significant. The R-squared from the output is 0.0527 which means that 5.27% of the variance of course evaluation is accounted for by the model.
The t-test for beauty is 3.18 and has a p-value of 0.002 which is less than 0.05 and hence it is statistically significant. Female has a t-test of -3.13, and has a p-value of 0.002 and hence it is statistically significant. However, beautyFE is not statistically significant with a t-test value of -1.50 and the p-value is 0.136 which is more than 0.05
The model predicts that when there is a unit increase in beauty there will be a significant increase in course evaluation by 0.1603508, a unit increase in female will cause a decrease in course evaluation by 0.1786041, and a unit increase in beautyFE will influence a decrease in course evaluation by 0.1102205. when all the independent variables are zero the value of course evaluation will be 4.110311.
g)

h)
From the output the predicted values have the same intercept, and the same slopes.
i)
prtest beauty_female == beauty_male

The lines from the predicted beauty for female and male are the same since they indicate not difference from the output.
j)
STATA OUTPUT
sdtest beauty_female == beauty_male

From the output it can be seen that the same slope since it doesn’t show any variation.