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 three independent variables X1, X2 and, X3. The following is a partial result of the regression analysis involving 20 observations.
F
$\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 20.00 & 5.00 \\\mathrm{X}_{1} & 15.00 & 3.00 \\\mathrm{X}_{2} & 8.00 & 5.00 \\\mathrm{X}_{3} & -18.00 & 10.00\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}\text { Source } & \text { DF } & \text { SS } & \text { MS } \\\text { Regression } & & & 80\\\text { Error }&&320\end{array}$ $\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 20.00 & 5.00 \\\mathrm{X}_{1} & 15.00 & 3.00 \\\mathrm{X}_{2} & 8.00 & 5.00 \\\mathrm{X}_{3} & -18.00 & 10.00\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}\text { Source } & \text { DF } & \text { SS } & \text { MS } \\\text { Regression } & & & 80\\\text { Error }&&320\end{array}$
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 β2 is significantly different from zero α = 0.05).
d. Perform a t test and determine whether or not β3 is significantly different from zero α = 0.05).
e. At α = 0.05, perform an F test and determine whether or not the regression model is significant.