Multiple Regression Analysis Was Used to Study the Relationship Between

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.
$\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 18.00 & 6.00 \\\mathrm{X}_{1} &12.00 & 8.00 \\\mathrm{X}_{2} & 24.00 & 48.00 \\\mathrm{X}_{3} &-36.00 & 36.00 \\\mathrm{X}_{4} &16.00 & 2.00\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}\text { Source } & \text { DF } & \text { SS } & \text { MS } &F\\\text { Regression } & & & 125\\\text { Error }&&\\\text { Total }&&760\end{array}$
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05).
c. Perform a t test and determine whether or not β4 is significantly different from zero α = 0.05).
d. At α = 0.05, perform an F test and determine whether or not the regression model is significant.