Multiple Regression Analysis Was Used to Study the Relationship Between $\beta$

Essay

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and four independent variables; X₁, X₂, X₃ and, X₄. The following is a partial result of the regression analysis involving 31 observations.

a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not $\beta$ ₁ is significantly different from zero ( $\alpha$ = 0.05).
c.Perform a t test and determine whether or not $\beta$ ₄ is significantly different from zero ( $\alpha$ = 0.05).
d.At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.