(i) Use OLS to estimate a model explaining colgpa using hsgpa, actmth, and acteng as independent variables. (Note: Use only observations where there is no missing data.)
The estimated equation is: colgpaˆ = β0 + β1 hsgpa + β2 actmth + β3 acteng
True or False: β1ˆ and β2ˆ are statistically significant at the 5% significance level against the two-sided alternative, but β3ˆ is not.
True
False
(ii) One standard deviation increase in hsgpa, that is about 0.343, (holding actmth and acteng fixed) the college GPA at the beginning of semester on average by approximately ____ points. The actmth would have to by approximately ____ standard deviations to change colgpaˆ by the same amount as one more standard deviation in hsgpa.
(iii) In terms of the parameters, which of the following is the null hypothesis in a test stating that actmth and acteng have the same effect (in the population) on colgpa?
H0: β2 ≠ β3
H0: β2 = β3
H0: β2 = 0, β3 = 0
H0: β2 ≠ 0, β3 ≠ 0
Suppose that θ = β2 − β3. Which of the following is the correct regression functional form that directly gives the t statistic for testing the null hypothesis that actmth and acteng have the same effect (in the population) on colgpa against a two-sided alternative?
colgpa = β0 + β1 hsgpa + θ actmth + β3 (actmth + acteng) + u
colgpa = β0 + β1 hsgpa + θ actmth + β3 actmth + acteng + u
colgpa = β0 + β1 hsgpa + β2 (actmth + acteng) + θ acteng + u
colgpa = β0 + β1 hsgpa + β2 actmth + acteng + θ acteng + u
colgpa = β0 + β1 hsgpa + θ actmth + β3 (actmth − acteng) + u
colgpa = β0 + β1 hsgpa + θ actmth + β3 actmth − acteng + u
colgpa = β0 + β1 hsgpa − θ actmth − β3 (actmth − acteng) + u
colgpa = β0 + β1 hsgpa − θ actmth − β3 actmth − acteng + u
Create a new variable actsm = actmth + acteng, and use OLS to estimate the following model:
colgpa = β0 + β1 hsgpa + θ actmth + β3 actsm + u
Estimated equation: colgpaˆ = β0ˆ + β1ˆ hsgpa + θˆ actmth + β3ˆ actsm
At the 5% significance level, you ____ the null hypothesis that actmth and acteng have the same effect (in the population) on colgpa against a two-sided alternative because the p-value of ____ is ____ than 0.05.
(iv) Suppose the college admissions officer wants you to use only the data from hsgpa, actmth, and acteng to develop a model that explains at least 50% of the variation in colgpa. It is enough to use only hsgpa, actmth, and acteng to obtain a model that explains more than 50% of the variation in colgpa.
True
False
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