A researcher studies the relationship between SAT scores, the test-taker’s family income (Income), and his/her grade point average (GPA). Data are collected from 24 students. A portion of the data is shown; the entire data set, labeled SAT, can be found on the text website.

Estimate: SAT = β₀ + β₁Income + β₂GPA + .

a. At the 5% significance level, are Income and GPA jointly and individually significant? Show the relevant steps of each test, using the critical value approach.

b. Predict SAT if Income is $80,000 and GPA is 3.5. Use these values for the explanatory variables to construct the 95% prediction interval for the individual SAT score.

Transcribed Image Text:

SAT 1651 1581 Income 47,000 34,000 GPA 2.79 2.97 1940 113,000 3.96