call : 1m(formula = rate ~ SAT + students, data = graduation) Residuals : Min 1Q Median 3Q Max -0. 118617 -0. 070890 -0. 000845 0. 047476 0.221380 coefficients : Estimate Std. Error t value pr(>|t|) (Intercept) -0. 6328254 0.1248549 -5. 068 6.82e-05 SAT 0 . 0010727 0 . 0001139 9. 417 1. 37e-08 students 0. 1679467 0. 0544246 3. 086 0. 00608 Residual standard error: 0. 08748 on 19 degrees of freedom Multiple R-squared: 0. 8425, Adjusted R-squared: 0. 8259 F-statistic: 50.82 on 2 and 19 DF, p-value: 2. 365e-0813) Conduct a test to determine if at least one of the explanatory variables are useful in predicting graduation rate. a. (2 points) In words, state the null and alternative hypotheses for this test. b. (1 point) Using the output from R, give the appropriate test-statistic with degrees of freedom c. (2 points) State your conclusion in terms of the problem supported with a p-value. 14) Conduct a test on the explanatory variable students to determine If It is a significant predictor of graduation rate in the presence of the other explanatory variable. a. (2 points) State the null and alternative hypotheses in statistical notation (notation does not have to be defined). b. (1 point) Using the output from R, give the test-statistic with degrees of freedom. c. (3 points) State a conclusion in the context of the problem supported with a p-value