ANLY 500 LABORATORY

This laboratory follows the exercises in the book, specifically the Performance Lawn Equipment Case Study homework assigned exercises Chapters 8 through and including 12, except this laboratory requires that you use R to complete the exercises. That is, you should answer all questions in the textbook exercises and complete computations using R. Each laboratory in ANLY 500 will build on the laboratories you have completed before. So, you will want to continue to keep your work in the folder you set-up for Laboratory #1 so that you can refer back to previous laboratories if necessary. You will also continue to use the data files for ANLY 500 on Moodle.

In reviewing the PLE data, Elizabeth Burke noticed that defects received from suppliers have decreased (DefectsAfterDelivery.csv data file). Upon investigation, she learned that in 2010, PLE experienced some quality problems due to an increasing number of defects in materials received from suppliers. The company instituted an initiative in August 2011 to work with suppliers to reduce these defects, to more closely coordinate deliveries, and to improve materials quality through reengineering supplier production policies. Elizabeth noted that the program appeared to reverse an increasing trend in defects; she would like to predict what might have happened had the supplier initiative not been implemented and how the number of defects might further be reduced in the near future.

In meeting with PLE’s human resources director, Elizabeth also discovered a concern about the high rate of turnover in its field service staff. Senior managers have suggested that the department look closer at its recruiting policies, particularly to try to identify the characteristics of individuals that lead to greater retention. However, in a recent staff meeting, HR managers could not agree on these characteristics. Some argued that years of education and grade point averages were good predictors. Others argued that hiring more mature applicants would lead to greater retention. To study these factors, the staff agreed to conduct a statistical study to determine the effect that years of education, college grade point average, and age when hired have on retention. A sample of 40 field service engineers hired 10 years ago was selected to determine the influence of these variables on how long each individual stayed with the company. Data are compiled in the Employee Retention worksheet.

Finally, as part of its efforts to remain competitive, PLE tries to keep up with the latest in production technology. This is especially important in the highly competitive lawn-mower line, where competitors can gain a real advantage if they develop more cost-effective means of production. The lawn-mower division therefore spends a great deal of effort in testing new technology. When new production technology is introduced, firms often experience learning, resulting in a gradual decrease in the time required to produce successive units. Generally, the rate of improvement declines until the production time levels off. One example is the production of a new design for lawn-mower engines.

To determine the time required to produce these engines, PLE produced 50 units on its production line; test results are given on the worksheet Engines in the database. Because PLE is continually developing new technology, understanding the rate of learning can be useful in estimating future production costs without having to run extensive prototype trials, and Elizabeth would like a better handle on this. Use techniques of regression analysis to assist her in evaluating the data in these three worksheets and reaching useful conclusions. Summarize your work in a formal report with all appropriate results and analyses.

As we found before, most of the work is getting the data into the proper format to analyze. This will still be true, even for performing regression analyses. So, the first thing to do to look at what the numbers of defects would have been if nothing had changed is to get a month number column along with that part of the DefectsAfterDelivery.csv data that is of interest. It looks like to me that the number of defects continues to rise through October 2011

To get the number of the month in a first column and the number of defects for that month in a second column I:

1. combine the years 2010 and 2011 into a vector, then remove the last two values because I’m not including November or December 2011.

2. create a month number vector for the 22 months of interest.

3. combine the month numbers and the number of defects into a matrix with two columns and check the first few rows.

4. Use the lm() function to do the regression and check the output.

5. Plot the data in a scatter plot, add the regression line and check it.

The question that you should answer at this point is why do we need to run an ANOVA on this data? You should say something in your lab report about whether you think it was necessary to do analysis of variance in this case or not.

In performing the regression analysis we always want to check and make sure that all the assumptions are true; linearity, normality of errors, equal variance or homoscedasticity, and independence. If we plot the residuals we see we are in trouble already. The plot of the residuals shown below has a pattern that to me looks cyclical. To create this plot I wrote another short R script. Note that to use the function xyplot() you will need to attach the lattice package again, i.e. library(lattice). The scrip and resulting plot are: