Exam 16: Inference for Regression

Interpret regression output. -A sales manager was interested in determining if there is a relationship between College GPA and sales performance among salespeople hired within the last year. A Sample of recently hired salespeople was selected the number of units each sold last Month recorded. Based on the regression results shown below, the residual standard Deviation is The regression equation is Units Sold $= - 0.48 + 7.42 \mathrm { GPA }$ Predictor Coef SE Coef T P Constant -0.484 3.256 -0.15 0.884 GPA 7.423 1.044 7.11 0.000 $S = 1.57429 \quad \mathrm { R } - \mathrm { Sq } = 78.38 \quad \mathrm { R } - S q ( a d j ) = 76.8\%$

Interpret confidence and prediction intervals. -An operations manager was interested in determining if there is a relationship between The amount of training received by production line workers and the time it takes for them To trouble shoot a process problem. A sample of recently trained line workers was Selected. The number of hours of training time received and the time it took (in minutes) For them to trouble shoot their last process problem were captured. The estimated Regression equation fit to the data was found to be significant at α = 0.05. The 95% Prediction interval for trouble shooting time with 8 hours of training was determined to Be 12.822 to 19.261. The correct interpretation is 19.261 minutes.

Write the null and alternative hypothesis.

Is there a significant relationship between time it takes to trouble shoot the process (minutes) and training received (use α = .05)? Give the appropriate test statistic, associated P-value and conclusion.

Predict the trouble shooting time for a line worker who received 8 hours of training.

Interpret a confidence interval for the slope of a regression equation. -A researcher decides to investigate his students' suspicions that longer essays receive Better scores on the SAT exam. He gathers data on the length of essays (number of lines) And the SAT scores received for a sample of students enrolled at his university. Based on His regression results, the 95% confidence interval for the slope of the regression equation Is -0.88 to 1.34. At α = 0.05, we can say

Are the assumptions / conditions for regression and inference satisfied? Explain.

Create a confidence interval for the slope of a regression equation. -An operations manager was interested in determining if there is a relationship between The amount of training received by production line workers and the time it takes for them To trouble shoot a process problem. A sample of 15 recently trained line workers was Selected. The number of hours of training time received and the time it took (in minutes) For them to trouble shoot their last process problem were captured. The regression output Is shown below. The 95% confidence interval for the slope of the regression equation is The regression equation is Trouble Shooting $= 30.7 - 1.84$ Training Predictor Coef SE Coef T P Constant 30.729 1.023 30.03 0.000 Training -1.8360 0.1376 -13.35 0.000 $S = 1.43588 \quad \mathrm { R } - \mathrm { Sq } = 93.28 \quad \mathrm { R } - \mathrm { Sq } ( \operatorname { adj } ) = 92.7 \%$

Is there a significant relationship between sales performance (units sold per month) and college GPA (use α = .05)? Give the appropriate test statistic, associated P-value and conclusion.

Check assumptions / conditions for inferences in regression. -Based on the plot of residuals versus fitted values below, we can say that

Are the assumptions / conditions for regression and inference satisfied? Explain.

Test for association. -As the carbon content in steel increases, its ductility tends to decrease. A researcher at A steel company measures carbon content and ductility for a sample of 15 types of steel Resulting in a correlation of -0.640. The calculated value of the t-statistic to test for a Significant association between carbon content and ductility is

Interpret regression output. -A sales manager was interested in determining if there is a relationship between College GPA and sales performance among salespeople hired within the last year. A Sample of recently hired salespeople was selected the number of units each sold last Month recorded. Based on the regression results shown below, the percentage of Variability in sales performance (units sold per month) accounted for by college GPA is The regression equation is Units Sold $= - 0.48 + 7.42 \mathrm { GPA }$ Predictor Coef SE Coef T P Constant -0.484 3.256 -0.15 0.884 GPA 7.423 1.044 7.11 0.000 $S = 1.57429 \quad \mathrm { R } - \mathrm { Sq } = 78.3 \% \quad \mathrm { R } - \mathrm { Sq } ( \operatorname { adj } ) = 76.8 \%$

Check assumptions / conditions for inferences in regression. -Based on the plot of residuals versus fitted values below, we can say that

Create a confidence interval for the slope of a regression equation. -As the carbon content in steel increases, its ductility tends to decrease. A researcher at A steel company measures carbon content and ductility for a sample of 15 types of steel. Based on these data he obtained the following regression results. The regression equation is Ductility $= 7.67 - 3.30$ Carbon Content Predictor Coef SE Coef T P Constant 7.671 1.507 5.09 0.000 Carbon Content -3.296 1.097 -3.01 0.010 $S = 2.36317 \quad \mathrm { R } - \mathrm { Sq } = 41.0 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 36.5 \%$ The 95% confidence interval for the slope of the regression equation is

Check assumptions / conditions for inferences in regression. -An operations manager was interested in determining if there is a relationship between The amount of training received by production line workers and the time it takes for them To trouble shoot a process problem. A sample of recently trained line workers was Selected. The number of hours of training time received and the time it took (in minutes) For them to trouble shoot their last process problem were captured. A regression equation Was fit to the data and the following histogram of residuals obtained. Based on this Histogram we can say

Predict the units sold per month for a new hire whose college GPA is 3.00.

What percentage of the variability in sales performance (units sold per month) can be accounted for by college GPA?

The confidence interval and prediction interval for trouble shooting time with 8 hours of training are shown below. Interpret both intervals in this context. 95\% CI 95\% PI (15.180,16.903) (12.822,19.261)

Check assumptions / conditions for inferences in regression. -An operations manager was interested in determining if there is a relationship between The amount of training received by production line workers and the time it takes for them To trouble shoot a process problem. A sample of recently trained line workers was Selected. The number of hours of training time received and the time it took (in minutes) For them to trouble shoot their last process problem were captured. A regression equation Was fit to the data and the following residual plot obtained. Based on this plot, we can Say