A company believes that there is a linear relationship between an employee’s hou
ID: 3055465 • Letter: A
Question
A company believes that there is a linear relationship between an employee’s hours of overtime for a particular week and the number of defective parts produced by that employee during that week. It therefore monitors the work of a sample of 15 employees, with results as shown in the table below.
As the plant engineer, you performed a regression analysis on the above data to examine the possible dependency of overtime (the independent variable) upon the number of defective parts (the dependant variable). The subsequent pages are the outputs (tabular and graphical) of such an analysis using the Regression capabilities of Excel (Tool/Data Analysis/Regression).
a. Are the company’s fears well founded? Provide a thorough explanation, including the regression model you are proposing, the statistical significance of the model, the correct interpretation of the model, any additional studies you believe necessary and other considerations you believe important in understanding the proposed model.
b. It is now the pre-holiday rush and your plant management is studying the probable impact of instituting a work week with 25 hours of overtime. What is the 95% confidence interval for the mean number of defects per worker likely to be produced at this level of overtime?
c. Your shop floor supervisor is an extremely sharp individual and is concerned with not only the average number of defects per worker, but with the number of defects produced by each worker. Provide a 95% prediction interval for the number of defects likely to be produced by a specific worker when working 25 hours of overtime.
SUMMARY OUTPUT Individual Overtime in Hours # of Defects w 2 Regression Statistics Multiple R 0.978499401 R Square 0.957461078 Adjusted R Square 0.954188853 Standard Error 3.061529145 Observations 3 15 5 7 11 7 ANOVA Regression Residual Total 1 13 14 MS F significance F 2742.551511 2742.552 292.6025 2.7033E-10 121.8484892 9.372961 2864.4 Intercept X Variable 1 Coefficients Standard Error tStat P-value 0.136830103 1.443630029 0.094782 0.925933 2.421465222 0.141559571 17.10563 2.7E-10 Lower 95% Upper 95% Lower 98.0% Upper 98.0% -2.981943 3.25560316 -3.6892283 3.962888457 2.11564436 2.72728608 2.04289334 2.796641111 15 X Variable 1 Line Fit Plot X Variable 1 Residual Plot 88,888 ???ps NO1 TTTTT 5 . 10 . 20 2 5 Predicted Y o 10 15 X Variable 1 20 25 X Variable 1Explanation / Answer
Solution:
a) Yes the company’s fear well founded because the regression model No of defects=-0.172+2.443*Overtime in Hours and the R2=0.956 which means the regression model explains 95.6% variability of the total variability. Since the p corresponding to F=262.026 is 1.622E-09 which is less than 0.05 at 5% level of significance therefore we reject the null hypothesis that the model is insignificant at 5% level of significance. I believe that there is no need of any information because the model explains the maximum variability.
b) 95% confidence interval for the mean number of defects when plant management is studying the probable impact of instituting a work week with 25 hours of overtime is
(55.315, 66.504).
c) 95% prediction interval for the number of defects likely to be produced by a specific worker when working 25 hours of overtime is (52.059, 69.760).
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.