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 $\beta$ ₁is 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 \9\alpha\) = 0.05,perform an F test and determine whether or not the regression model is significant.