Multiple regression is used to model y = annual income using x₁ = number of years of education and x₂ = number of years employed in current job.
a. It is possible that the coefficient of x₂ is positive in a simple regression but negative in multiple regression.
b. It is possible that the correlation between y and x₁ is 0.30 and the multiple correlation between y and x₁ and x₂ is 0.26.
c. If the F statistic for H₀: β₁ = β₂ = 0 has a P-value = 0.001, then we can conclude that both predictors have an effect on annual income.
d. If β₂ = 0, then annual income is independent of x₂ in simple regression.