(A)Estimate a Simple Linear Regression Model Using the Sample Data

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The Answer is (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 10^th employee 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 X and 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).

(A)Estimate a Simple Linear Regression Model Using the Sample Data

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