Each year U.S. News and World Report conducts its \"Survey of America\'s Best Gr

Question

Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and Professional Schools." and ranks the top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. The results of a simple linear regression of SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance?

a = -92040 b = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67

Explanation / Answer

As there is only one predictor variable, so F-test of significance of the model is equivalent to t-test of the significance of coefficient of GMAT score(b). We have been supplieed the t-statistic = 6.67 and degress of freedom of t-stat is 23. So we will test the significance of t-statistic at 5% level of significance assuming null hypothesis is that the coefficient is zero , i.e GMAT score is of no importance to predict SALARY.

As the alternative is both sided so the critical value of the t-statistic will be the (1-0.05/2) = 97.5 th percentile of t-distribution with 23 degrees of freedom. which is equal to 2.069

As the value of t-statistic = 6.67 > 2.069 = crictical value, at 5% elvel of significance we reject the null hypothesis to conclude that there is a sufficient evidence to suggest that GMAT score has a sginificant importance in predicting SALARY via linear regression model.

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