(B) Perform an F-test for the existence of a linear relationship between Yand X. Use a 5% level of significance. (C) Plot the fitted values versus residuals associated with the model in Question 119. What does the plot indicate? (D) How do you explain the results you have found in (A) through (C)? (E) Suppose you learn that the 10themployee in the sample has been fired for missing an excessive number of work-hours during the past year. In light of this information, how would you proceed to estimate the relationship between the number of work-hours an employee misses per year and the employee’s annual wages, using the available information? If you decide to revise your estimate of this regression equation, repeat (A) and (B)ANS: (A)
The simple linear regression model is=218.35 – 9.5775 (Annual Wages). The fit of this estimated model is pretty poor; the percent variation explained is only 0.0886. (B) Since the p-value = 0.2814 is well above 0.05, this indicates that there is no linear relationship between Y(work hours missed) and X(employee’s annual wages). (C) The chart of residuals versus fitted values points to an obvious outlier associated with the 10themployee in the sample who has missed 485 hours of work (for this employee, fitted value = 101.5 and residual = 383.5). (D) Since there is no evidence of a linear relationship between Xand Y, and the existence of an obvious outlier, the estimated linear regression model in (A) provides a very poor fit to the data. (E) We should eliminate the data point associated with this employee and rerun the regression in (A) and (B). We expect to obtain much better results.
The simple linear regression model is=193.6 – 9.79 (Annual Wages). The fit of this estimated model is much better than the one obtained in (A). The percentage of variation explained has improved from only 0.0886 to 0.4949. In addition, with the revised model, the p-value = 0.005 is well below 0.05, which indicates that there is a linear relationship between Y(work hours missed) and X(employee’s annual wages). This also confirms what we expect to see, intuitively; as wages increase, worker hours missed decreases (i.e., slope is negative).PTS: 1 MSC: AACSB: Analytic | AACSB: Regression AnalysisNARRBEGIN: SA_124_126 The manager of a commuter rail transportation system was recently asked by his governing board to predict the demand for rides in the large city served by the transportation network. The system manager has collected data on variables thought to be related to the number of weekly riders on the city’s rail system. The table shown below contains these data.
The variables “weekly riders” and “population” are measured in thousands, and the variables “price per ride”, “income”, and “parking rate” are measured in dollars. NARREND 12. (A) Estimate a multiple regression model using all of the available explanatory variables.
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- Regression Analysis, d. multicollinearity