A researcher studies the relationship between SAT scores,the test-taker's family income,and his or her grade point average (GPA).Data are collected from 24 students.He estimates the following model: SAT = β₀ + β₁ GPA + β₂ Income + ε.The following table summarizes a portion of the regression results. Which of the following is the correct hypotheses for testing the joint significance? A) H₀:β₀ = β₂ = 0;H_A: At least β₀ ≠ 0 B) H₀:β₁ = β₂ = 0;H_A: At least one β_j ≠ 0 C) H₀:β₀ = β₁ = β₂ = 0;H_A: All β_j ≠ 0 D) H₀:β₁ = β₂ = 0;H_A: Both β_j ≠ 0

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The hypotheses for testing the joint significance of SAT, family income and GPA are given by H₀: β₁ = β₂ = 0 (null hypothesis) and H_A: At least one β_j ≠ 0 (alternative hypothesis). Choice B correctly represents these hypotheses. Choices A, C, and D do not correctly state the null and alternative hypotheses for testing the joint significance.

A Researcher Studies the Relationship Between SAT Scores,the Test-Taker's Family