Question: A certain college administrator is interested in seeing whether math (X₁) and verbal (X₂) SAT scores are the better predictor of performance in a required freshman history course. The data are in the file (data_prob_2.xls).

a) State the multiple regression equation.

b) Interpret the meaning of the slopes b₁ and b₂ in the model.

c) Interpret the meaning of the regression coefficient b₀.

d) Test H₀: ?₂ = 0 against H₁: ?₂ > 0. Interpret your finding.

e) Use a 95% confidence interval to estimate ?₂. Interpret the p-value corresponding to the estimate ?₂. Does the confidence interval support your interpretation in d)?

f) Determine the coefficient of multiple determination r²_Y.12 and interpret its meaning.

g) Perform a residual analysis on your results and determine the adequacy of the fit of the model.

h) Plot the residuals against the prices. Is there evidence of a pattern in the residuals? Explain.

i) When you compare the results in [2] with (a), what do you think the effect of math scores on history scores? For example, if you and I both have 570 verbal SATs, but you have a 740 math SAT and I have only a 520 SAT, what do you think would happen if simple regression or multiple regression analyses are applied?