Question

On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that predict a student's score on the final exam. She collects data from 60 students, a portion of which is shown in the accompanying table Final 94 74 Math 92 90 Hours 63 64 icture Click here for the Excel Data File a. Estimate the sample regression equation that enables us to predict a student's final exam score on the basis of his/her math score and the number of hours studied per week. (Round your answers to 2 decimal places.) Final =L + Math + Hours b-1. At the 5% significance level, are a student's math score and the number of hours studied per week jointly significant in explaining a student's final exam score? First, specify the competing hypotheses H0: β1 -β2-0 ; HA: At least one ßj > 0 0 ßj < 0 0 H0: β1 -β2-0 ; HA: At least one ßj z 0 β2-0 ; HA: At least one H0: β1 b-2. Find the p-value O p-value< 0.01 0.01 s p-value <0.025 0.025 s p-value<0.05 0.05 s p-value< 0.10 O o-value 2 0.10

Answer 1

EXCEL output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.811640501 0.658760303 0.64678698 5.540938014 60 ANOVA Significance F 2 3378.386338 1689.193 55.01901 4.92263E-14 df MS Regression Residual Total 57 1750.013662 30.70199 59 5128.4 Coefficients Standard Error tstat P-value Lower 95% Upper 95% 40.548214813.371227665 12.02773 2.83E-17 33.79744791 47.29898171 0.2488797770.041058442 6.061598 1.14E-07 0.166661667 0.331097888 4.851901363 0.568694556 8.531647 9.06E-12 3.713110166 5.99069256 Intercept Math Hours The regression equation is Final 40.55 +0.25Math +4.85Hours (b-1). H o: A-A = 0, H. At least one β 0

(b-2). P-value < 0.01. (b-3). Reject Ho, we can conclude the explanatory variables are jointly significant. (c-2) Explanatory variables p-value Significant in Explaining Final Score Significant Significant Math Hours