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 three independent variables X₁, X₂ and, X₃. The following is a partial result of the regression analysis involving 20 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 $\beta$ ₂ is significantly different from zero ( $\alpha$ = 0.05).
d.Perform a t test and determine whether or not $\beta$ ₃ is significantly different from zero ( $\alpha$ = 0.05).
e.
At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.