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Use the data set GPA1 to answer this question. It was used in Computer Exercise C13 in Chapter 3 to

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Use the data set GPA1 to answer this question. It was used in Computer Exercise C13 in Chapter 3 to estimate the effect of PC ownership on college GPA.

(i) Run the regression colGPA on PC, hsGPA, and ACT and obtain a 95% confidence interval for bPC. Is the estimated coefficient statistically significant at the 5% level against a two-sided alternative?

(ii) Discuss the statistical significance of the estimates β̂hsGPA and β̂hACT in part (i). Is hsGPA or ACT the more important predictor of colGPA?

(iii) Add the two indicators fathcoll and mothcoll to the regression in part (i). Is either individually significant? Are they jointly statistically significant at the 5% level?

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i The 95 confidence interval around PC is 0 044 0 271 The coefficient estimate of 0 157 is statistically different from zero at the 5 level against a two sided alternative ii While the coefficient on hsGPA is statistically significant that on ACT is not statistically different from 0 at the 5 level The 95 confidence interval for hsGPA is 0 262 0 632 while the 95 confidence interval for ACT is 0 012 0 029 That these intervals do not overlap suggests that the marginal effect of a 1 unit change in hsGPA on colGPA is larger in magnitude than the marginal effect of a 1 unit change in ACT score iii Neither fathcoll or mothcoll are individually significant at the 5 level t statistics of 0 68 and 0 06 respectively We can test joint significance using an F test Our unrestricted model including fathcoll and mothcoll yields SSR r 15 149 Our restricted model fathcoll mothcoll 0 has SSR ur 15 094 The F test for the joint significance of fathcoll and mothcoll is The p value for this F statistic …View the full answer


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Introductory Econometrics A Modern Approach

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Question Details
Chapter # 4
Section: Computer Exercises
Problem: 13
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Question Posted: July 02, 2020 04:13:48
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