3. You are working with college admission data and trying to determine whether you can predict a student’s future GPA based upon their college admission test score. The test is scored on a scale of 0–100, while GPA is measured on a scale of 0.0–4.0.

Call:

lm(formula = gpa ~ test)

Residuals:

Min 1Q Median 3Q Max

-0.3050 -0.1237 0.0525 0.1412 0.2000 Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.695000 0.531954 1.307 0.2392 test 0.033000 0.006205 5.318 0.0018 **

When you build your regression model, you receive the following results:
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.1962 on 6 degrees of freedom Multiple R-squared: 0.825, Adjusted R-squared: 0.7958 F-statistic: 28.29 on 1 and 6 DF, p-value: 0.001798

a. According to this model, what impact would a single point increase in admissions test score have on the prediction of a student’s GPA?

b. If a student scored 82 on the admissions test, what would be your prediction of their GPA?

c. If another student scored 97 on the admissions test, what would be your prediction of their GPA?

d. How well does this model fit the data based upon the Adjusted R-squared?