A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).
Based on the output, how much of the variability in Turnover Rate is explained by the
Estimated multiple regression model? $$\begin{array}{l}
\text { Dependent Variable is Turnover Rate }\
\begin{array} { l r r r r }
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \
\text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \
\text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000
\end{array}
\end{array}$$
A) 78.3%
B) 79.6%
C) 12.1%
D) 95.4%
E) None of the above.

Question

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).
Based on the output, how much of the variability in Turnover Rate is explained by the
Estimated multiple regression model? $$\begin{array}{l}
\text { Dependent Variable is Turnover Rate }\
\begin{array} { l r r r r } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \
\text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \
\text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000
\end{array}
\end{array}$$
A) 78.3%
B) 79.6%
C) 12.1%
D) 95.4%
E) None of the above.

Quizplus · Accepted Answer

To determine the amount of variability in Turnover Rate explained by the estimated multiple regression model, we need to look at the R-squared value. The R-squared value is the proportion of variance in the dependent variable (Turnover Rate) that is explained by the independent variables (Trust Index and Average Bonus). In this case, the R-squared value is not given directly in the output, but it can be calculated using the adjusted R-squared value, which is given as 0.7864.

The adjusted R-squared value is a corrected version of the R-squared value that takes into account the number of independent variables in the model. The formula to calculate R-squared is:

R-squared = 1 - (SSresid / SStotal)

where SSresid is the sum of squared residuals (the variation that is not explained by the model) and SStotal is the total sum of squares (the variation in the dependent variable).

The adjusted R-squared value can be calculated using the formula:

adjusted R-squared = 1 - [(1 - R-squared)(n - 1) / (n - k - 1)]

where n is the sample size and k is the number of independent variables.

Using the given values in the output, we can calculate the R-squared value as:

R-squared = 1 - (363.614 / 1676.804) = 0.7847

Then, using the sample size of 33 and the 2 independent variables, we can calculate the adjusted R-squared value as:

adjusted R-squared = 1 - [(1 - 0.7847)(33 - 1) / (33 - 2 - 1)] = 0.7864

Therefore, the amount of variability in Turnover Rate explained by the estimated multiple regression model is 78.6%, which is closest to option B (79.6%).

A Sample of 33 Companies Was Randomly Selected and Data