Question

Directions: Please download the files, HW_6_Data.xlsx, from Blackboard. This question requires you to use Excel to run multiple linear regression models. In order to receive full credit, you must turn in Excel output with your answers. A researcher was interested in how students' Graduate Record Examinations scores (GREQ- Quantitative and GREV-Verbal) predict college students' graduate school Grade Point Average (GGPA). He collects data from 30 college students. The GRE Quantitative (X1) and GRE Verbal (X2) scores can range from 400-1600 (Note. This is the old GRE score scale). GGPA (Y) can range from 0.00 to 4.00.

Answer 1

EXCEL (Data Analysis) output: SUMMARY OUTPUT Regression Statistics Multiple R 0.54210699 R Square 0.293879989 Adjusted R Square 0.241574803 Standard Error 0.584144747 Observations 05911 30 ANOVA df Significance F 0.009117169 Regression Residual Total 2 27 29 SS MS F 3.834389359 1.917195 5.618563 9.213077307 0.341225 13.04746667 Intercept GREQ GREV Coefficients -1.321598799 0.005620308 0.001733925 Standard Error t Stat p-value Lower 95% Upper 95% 1.278917315 -1.03337 0.310597 -3.945720344 1.302522745 0.002524787 2.226052 0.03455 0.000439873 0.010800742 0.001478294 1.172923 0.251071 -0.001299284 0.004767134 The proportion of variance is R2 = 0.294

The unexplained variation in the regression model is 1-R2 =1-0.294 = 0.706. h) The value of test statistic is F=5.62. The numerator degrees of freedom is 2. The denominator degrees of freedom is 27. The test statistic for GREQ is t = 2.23 The test statistic for GREV is t=1.17. Since p-value = 0.0091), then reject the null hypothesis. Therefore, the regression coefficients for GREQ and GREV are significant.