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C291FE2012_FinalVersion_Apr9

# The data and some of the excel regression results are

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troubleshoot their last process problem were recorded. The data and some of the Excel regression results are shown below. The scatterplot and Regression Statistics have been withheld. Hours of Training 8 1 0 9 7 7 5 4 5 1 0 1 1 4 4 2 8 1 0 Troubleshoot time (min) 1 5 1 1 1 6 1 8 1 9 2 0 2 6 2 2 1 2 1 1 2 2 2 1 2 8 1 7 1 2 ANOVA Df SS MS F Significance F Regression 1 367.20 367.20 178.10 .000 Residual 13 26.80 2.06 Total 14 394.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 30.729 1.023 30.03 0.000 Training -1.8360 0.1376 -13.35 0.000 a) Write the equation of the estimated least squares regression line. b) Interpret the coefficient of Training . [Don’t just say it is the slope!] c) Test the hypothesis of no linear relationship between troubleshooting time and hours of training. (Note: You have a choice of two test statistics in the output to test this; use either one.). Write the hypotheses, the value of the test statistic, the P-value and the conclusion. Hypotheses: H 0 : _________________ H a : _________________ Test statistic value = _____________ P-value = _____________ Conclusion (Be specific and be concise – use one sentence only): d) What percentage of variation in troubleshooting time is explained by the number of hours of training? Report your answer to the nearest whole number. 13

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e) Compute the sample correlation coefficient between X and Y. Report it as a percentage to the nearest whole number. f) Construct an exact 95% confidence interval for the slope of the regression line. [Note: “exact” means that you need to look up the exact multiplier in the tables] Report your answer using four decimal places, with the format (x.xxxx , x.xxxx). g) From the confidence interval you computed in part f), can you conclude that the average troubleshooting time is reduced by at least one minute for each additional hour of training time? Explain, in one sentence only . h) Compute the estimated standard deviation of the residuals, which is denoted by ‘ s e ’ in our notes and the text. Report your answer to three decimal places. i) Compute an approximate 95% prediction interval for the troubleshooting time required by a worker who receives six hours of training time. [Remember: “Approximate” means to ignore the extrapolation penalty term and 1/n term and use an approximate multiplier.] Report your answer using three decimal places, with the format (x.xxx , x.xxx). j) From the residual plot below we can say that...: __ A. ... the nearly normal condition is satisfied. __ B. ... the nearly normal condition is not satisfied. __ C. ... the equal spread condition is satisfied. __ D. ... the linearity condition is not satisfied. __ E. ... the independence assumption is not satisfied. 15

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Question 8. (Total 12 marks) “How to ‘excel’ at regression” A financial analyst wanted to examine the relationships between salary in (\$1000) and four variables: age, experience in the field, number of degrees, and number of previous jobs in the field. He took a random sample of 20 employees and obtained the following Excel output. Regression Statistics Multiple R 0.7647 R Square 0.5848 Adjusted R Square 0.4741 Standard Error 6.5266 Observations 20 ANOVA Df SS MS F Significance F Regression 4 899.8545 224.9636 5.2813 0.0074 Residual 15 638.9455 42.5964 Total 19 1538.8000 Coefficients Standard Error t Stat P-value Intercept 13.2724 12.9420 1.0255 0.3214 AGE 1.3052 0.3071 4.2507 0.0007 EXPERIENCE -1.0195 0.4425 -2.3037 0.0360 DEGREES 2.8940 2.2162 1.3059 0.2113 PREVJOBS -0.6081 1.6843 -0.3611 0.7231 a) What are the null and alternative hypotheses that are tested by the F-stat of 5.2813?
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