Whittenberg Distributors,a major retailing and mail-order operation,has been in business for the past 10 years.During that time,its mail-order operations have grown from a sideline to represent more than 80 percent of the company's annual sales.Of course,the company has suffered growing pains.At times,overloaded or faulty computer programs resulted in lost sales.And scheduling temporary workers to augment the permanent staff during peak periods has always been a problem.Peter Bloom,manager of mail-order operations,has developed procedures for handling most problems.However,he is still trying to improve the scheduling of temporary workers to take customer telephone orders.Under the current system,Peter keeps a permanent staff of 60 employees who handle the base telephone workload and supplements this staff with temporary workers as needed.The temporary workers are hired on a daily basis;he determines the number needed for the next day the afternoon before based on his estimate of the upcoming telephone volume.Peter has decided to try regression analysis to improve the hiring of temporary workers.By summarizing the daily labor-hours into weekly totals for the past year,he determined the number of workers used each week.In addition,he listed the number of orders processed each week.After entering the data into a spreadsheet,Peter ran two regressions.Regression 1 related the total number of workers (permanent staff plus temporary workers)to the number of orders received.Regression 2 related only temporary workers to the number of orders received.The output of these analyses follows: Regression model: W = a + b * T where: W = workers;T = telephone orders

Question

Quizplus · Accepted Answer

Required:
(1)Peter Bloom estimates that Whittenberg Distributors will receive 12,740 orders during the second week of December.
(a)Predict the number of temporary workers needed for this week using regression 1.Round your answer to the nearest whole number.
(b)Using regression 2,predict the number of temporary workers needed during this week.Round your answer to the nearest whole number.
(2)Which of the two regression analyses appears to be better? Explain your answer.
(3)Describe at least three ways that Peter Bloom could improve his analysis to make better predictions than either of these regression results provides.(CMA Adapted)
Please see Feedback for answers.
 Feedback: (1)(a)Using the regression results relating total workers to the number of orders received (Regression I),the number of temporary workers needed is 17,calculated as follows:
W = a + bT
= 21.938 + .0043 (12,740)
= 76.720 (Round to 77)
Total workers needed 77
Less permanent workers 60
Temporary workers 17
(b)Using the regression analysis that relates the number of temporary workers to the number of orders received (Regression 2),the number of temporary workers needed is 19,calculated as follows:
W = a + bT
= -46.569 + .0051 (12,740)
= 18.405
Temporary workers = 19 (rounded)
(2)Regression Analysis 2 appears to be better for the following reasons.
- The standard error of the estimate is lower for Regression 2 (1.495 vs.3.721)which usually means that the prediction is expected to be more accurate.However,note that the dependent variable in Regression 2 (temporary workers)is on the average somewhat smaller (about 1/4)that of regression 1 (total workers),so that the standard errors are not directly comparable.Because the dependent variable for Regression 2 is smaller,we would expect the standard error also to be smaller.Bloom needs to compare the SE to the mean of the dependent variable (not available in this case)to further understand whether the regressions provide useful predictions
- The coefficient of determination is higher for Regression 2 (.755 vs..624)which indicates a more reliable regression model;the R Squared values are OK but not particularly strong.
- The t-value is slightly higher for regression 2 (2.04 vs.1.95 for regression 1);neither t-value is particularly good,an indication of a weak relationship between the independent variable and the dependent variable.
- Since both the regressions are quite similar,Bloom should consider why one should lead to better results than the other.That is,could not Bloom argue that regression 1 is preferred on the logical basis that there should be a stronger relationship between total orders and total number of workers? Even if the statistical measures are more favorable for regression 2,regression 1 might be preferable because it represents a more plausible relationship.Since any regression is based on a sampling of data observations,it might be that if several regressions were done over many time periods,the regression 1 model would show better statistical measures.
(3)At least three ways that Peter Bloom could improve his analysis in order to get better predictions are described below.
- Perform regression calculations on a daily rather than weekly basis,since Bloom is analyzing the need for temporary workers on a daily rather than a weekly basis.
- Note the comment (in part 2 above)about the need for further data analysis to examine the value of regression 1 versus regression 2.
- Run the regression on data for more than one year if this data is available.If the historical data
is a good indicator of future trends,this will result in better predictions of expected orders.If several months of data are used,Bloom should make sure that there are no shifts or cyclical changes in the data over this longer period of time.
- Graph the data and look for outliers and other signs of non-linearity;note however that the Durbin Watson statistics for both regressions are in the OK range.
- Study the data for seasonality and modify the model if appropriate.

Whittenberg Distributors,a Major Retailing and Mail-Order Operation,has Been in Business