Question
The personnel department of a certain industrial firm used 12 subjects in a study to determine the relationship between job performance rating $(y)$ and scores of four tests. The data are as follows \begin{tabular}{ccccc} $\boldsymbol{y}$ & $\boldsymbol{x}_{1}$ & $\boldsymbol{x}_{2}$ & $\boldsymbol{x}_{3}$ & $\boldsymbol{x}_{4}$ \\ \hline 11.2 & 56.5 & 71.0 & 38.5 & 43.0 \\ 14.5 & 59.5 & 72.5 & 38.2 & 44.8 \\ 17.2 & 69.2 & 76.0 & 42.5 & 49.0 \\ 17.8 & 74.5 & 79.5 & 43.4 & 56.3 \\ 19.3 & 81.2 & 84.0 & 47.5 & 60.2 \\24.5 & 88.0 & 86.2 & 47.4 & 62.0 \\ 21.2 & 78.2 & 80.5 & 44.5 & 58.1 \\ 16.9 & 69.0 & 72.0 & 41.8 & 48.1 \\ 14.8 & 58.1 & 68.0 & 42.1 & 46.0 \\ 20.0 & 80.5 & 85.0 & 48.1 & 60.3 \\ 13.2 & 58.3 & 71.0 & 37.5 & 47.1 \\ 22.5 & 84.0 & 87.2 & 51.0 & 65.2 \end{tabular}Estimate the regression coefficients in the model$\hat{y}=b o+b_{1} x_{1}+b_{2} x_{2}+b_{3} x_{3}+b_{4} x_{4}$.
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Step 1: First, we need to calculate the means of $y$, $x_1$, $x_2$, $x_3$, and $x_4$. Show more…
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6. The personnel department of a certain industrial firm used 12 subjects in a study to determine the relationship between job performance rating (y) and scores on four tests (x1, x2, x3, x4). The multiple linear regression results are as follows: Call: lm(formula = Rating ~ X1 + X2 + X3 + X4, data = ratings) Residuals: Min 1Q Median 3Q Max -1.6462 -0.8679 0.1327 0.7277 1.3610 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.32046 9.36616 0.355 0.7334 X1 0.42105 0.13265 3.174 0.0156 * X2 -0.29578 0.23179 -1.276 0.2426 X3 0.01638 0.24810 0.066 0.9492 X4 0.12465 0.24197 0.515 0.6223 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.222 on 7 degrees of freedom Multiple R-squared: 0.939, Adjusted R-squared: 0.9042 F-statistic: 26.94 on 4 and 7 DF, p-value: 0.0002402 Comment on the relationship between the test scores and job performance, as well as on the quality of the model fit.
The personnel director for Electronics Associates developed the following estimated regression equation relating an employee's score on a job satisfaction test to his or her length of service and wage rate. \[ \hat{y}=14.4-8.69 x_{1}+13.5 x_{2} \] where \[ \begin{array}{l} x_{1}=\text { length of service (years) } \\ x_{2}=\text { wage rate (dollars) } \end{array} \] $y=$ job satisfaction test score (higher scores indicate greater job satisfaction) a. Interpret the coefficients in this estimated regression equation. b. Develop an estimate of the job satisfaction test score for an employee who has four years of service and makes $\$ 6.50$ per hour.
The personnel director for Electronics Associates developed the following estimated regression equation relating an employee's score on a job satisfaction test to his or her length of service and wage rate. $$\hat{y}=14.4-8.69 x_{1}+13.5 x_{2}$$ where $\begin{aligned} x_{1} &=\text { length of service (years) } \\ x_{2} &=\text { wage rate (dollars) } \\ y &=\text { job satisfaction test score (higher scores } \end{aligned}$ indicate greater job satisfaction) a. Interpret the coefficients in this estimated regression equation. b. Predict the job satisfaction test score for an employee who has four years of service and makes $\$ 6.50$ per hour.
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