Question: The following equations were estimated using the
The following equations were estimated using the data in ECONMATH, with standard errors reported under coefficients. The average class score, measured as a percentage, is about 72.2; exactly 50% of the students are male; and the average of colgpa (grade point average at the start of the term) is about 2.81. ![The following equations were estimated using the data in ECONMATH, with standard errors reported under coefficients. The average class score, measured as a percentage, is about 72.2; exactly 50% of the students are male; and the average of colgpa (grade point average at the start of the term) is about 2.81.
(i) Interpret the coefficient on male in the second equation and construct a 95% confidence interval for bmale. Does the confidence interval exclude zero?
(ii) In the second equation, how come the estimate on male is so imprecise? Should we now conclude that there are no gender differences in score after controlling for colgpa? [Hint: You might want to compute an F statistic for the null hypothesis that there is no gender difference in the model with the interaction.]
(iii) Compared with the third equation, how come the coefficient on male in the last equation is so much closer to that in the second equation and just as precisely estimated?](../images/the-following-equations-were-estimated-using-the-data-in-econmath-with-65341-1.jpg)
![The following equations were estimated using the data in ECONMATH, with standard errors reported under coefficients. The average class score, measured as a percentage, is about 72.2; exactly 50% of the students are male; and the average of colgpa (grade point average at the start of the term) is about 2.81.
(i) Interpret the coefficient on male in the second equation and construct a 95% confidence interval for bmale. Does the confidence interval exclude zero?
(ii) In the second equation, how come the estimate on male is so imprecise? Should we now conclude that there are no gender differences in score after controlling for colgpa? [Hint: You might want to compute an F statistic for the null hypothesis that there is no gender difference in the model with the interaction.]
(iii) Compared with the third equation, how come the coefficient on male in the last equation is so much closer to that in the second equation and just as precisely estimated?](../images/the-following-equations-were-estimated-using-the-data-in-econmath-with-65341-2.jpg)
(i) Interpret the coefficient on male in the second equation and construct a 95% confidence interval for bmale. Does the confidence interval exclude zero? (ii) In the second equation, how come the estimate on male is so imprecise? Should we now conclude that there are no gender differences in score after controlling for colgpa? [Hint: You might want to compute an F statistic for the null hypothesis that there is no gender difference in the model with the interaction.] (iii) Compared with the third equation, how come the coefficient on male in the last equation is so much closer to that in the second equation and just as precisely estimated?
Transcribed Image Text:
score = 32.31 + 14.32 colgpa (2.00) (0.70) n = 856, R² = .329, R² = .328. score = 29.66 + 3.83 male + 14.57 colgpa (2.04) (0.74) (0.69) n = 856, R² = .349, R² = .348. %3D score = 30.36 + 2.47 male + 14.33 colgpa + 0.479 male·colgpa (2.86) (3.96) (0.98) (1.383) = 856, R² .349, R? = .347. n 30.36 + 3.82 male + 14.33 colgpa + 0.479 male · (colgpa – 2.81) (2.86) (0.74) score = (0.98) (1.383) n = 856, R² .349, R? = .347.
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