Multiple Regression Analysis Was Used to Study the Relationship Between

question 40

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.

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Definitions:

Extinction

In psychology, the gradual weakening and disappearance of a conditioned response.

Punishing

The act of imposing a penalty or negative consequence on an individual or group to reduce or eliminate undesirable behavior.

Misbehavior

Actions or conduct that are inappropriate or violate social norms or rules.

Delay

The act of postponing or making something happen later than originally planned.