A random sample of 30 college students yielded data on Y = grade in an introductory college chemistry course (four-point scale), X₁ = high school GPA (four-point scale), and X₂ = SAT score (2400 maximum). The standard errors are in parentheses, the t values are in brackets, and R₂ = 0.22.

a. Explain why you either agree or disagree with this interpretation: “The primary implication of these results is that high school GPA and SAT score are poor predictors of a student’s success in this chemistry course.”

b. Suppose that an important omitted variable is X₃ = 1 if the student has taken a high school chemistry course, 0 otherwise; the true coefficients of X₁, X₂, and X₃
are positive; and X₃ is negatively correlated with X1 and uncorrelated with X₂.
If so, is the estimated coefficient of X₁ in the preceding equation biased upward or downward? Be sure to explain your reasoning.

Transcribed Image Text:

Y=-4.20 +2.79X1+0.0027X2 (5.88) (1.05) (0.0033) [0.72] [2.64] [0.83]