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. score = 32.31 + 14.32 colgpa (2.00) (0.70) n = 856, R² = .329, R = .328. 29.66 + 3.83 male + 14.57 colgpa score = (2.04) (0.74) (0.69) n = 856, R? = .349, R = .348. score = 30.36 + 2.47 male + 14.33 colgpa + 0.479 male· colgpa (2.86) (3.96) (0.98) (1.383) 856, R? = .349, R = .347. score = 30.36 + 3.82 male + 14.33 colgpa + 0.479 male· (colgpa – 2.81) (2.86) (0.74) (0.98) (1.383) n = 856, R? = .349, R = .347. (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, why is the estimate on male 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, why is the coefficient on male in the last equation so much closer to that in the second equation and just as precisely estimated?
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. score = 32.31 + 14.32 colgpa (2.00) (0.70) n = 856, R² = .329, R = .328. 29.66 + 3.83 male + 14.57 colgpa score = (2.04) (0.74) (0.69) n = 856, R? = .349, R = .348. score = 30.36 + 2.47 male + 14.33 colgpa + 0.479 male· colgpa (2.86) (3.96) (0.98) (1.383) 856, R? = .349, R = .347. score = 30.36 + 3.82 male + 14.33 colgpa + 0.479 male· (colgpa – 2.81) (2.86) (0.74) (0.98) (1.383) n = 856, R? = .349, R = .347. (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, why is the estimate on male 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, why is the coefficient on male in the last equation so much closer to that in the second equation and just as precisely estimated?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text: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.
score = 32.31 + 14.32 colgpa
(2.00) (0.70)
n = 856, R² = .329, R = .328.
29.66 + 3.83 male + 14.57 colgpa
score =
(2.04) (0.74)
(0.69)
n = 856, R? = .349, R = .348.
![score = 30.36 + 2.47 male + 14.33 colgpa + 0.479 male· colgpa
(2.86) (3.96)
(0.98)
(1.383)
856, R? = .349, R = .347.
score = 30.36 + 3.82 male + 14.33 colgpa + 0.479 male· (colgpa – 2.81)
(2.86) (0.74)
(0.98)
(1.383)
n = 856, R? = .349, R = .347.
(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, why is the estimate on male 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, why is the coefficient on male in the last equation so much
closer to that in the second equation and just as precisely estimated?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e2a76e8-39a2-41b2-9c0a-279511c55c09%2Fb70f5048-34ac-4f7c-b242-83112b638c8b%2Fftqv4r9.png&w=3840&q=75)
Transcribed Image Text:score = 30.36 + 2.47 male + 14.33 colgpa + 0.479 male· colgpa
(2.86) (3.96)
(0.98)
(1.383)
856, R? = .349, R = .347.
score = 30.36 + 3.82 male + 14.33 colgpa + 0.479 male· (colgpa – 2.81)
(2.86) (0.74)
(0.98)
(1.383)
n = 856, R? = .349, R = .347.
(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, why is the estimate on male 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, why is the coefficient on male in the last equation so much
closer to that in the second equation and just as precisely estimated?
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