Reference no: EM133471975

Case: Performance Lawn Equipment (PLE), headquartered in St. Louis, Missouri, is a privately owned designer and producer of traditional lawn mowers used by homeowners. In the past 10 years, PLE has added another key product, a medium-size diesel power lawn tractor with front and rear power takeoffs, Class I three-point hitches, four-wheel drive, power steering, and full hydraulics. This equipment is built primarily for a niche market consisting of large estates, including golf and country clubs, resorts, private estates, city parks, large commercial complexes, resorts, private estates, city parks, lawn care service providers, etc. PLE provides most of the products to dealerships, which, in turn, sell directly to end users. PLE employs 1,660 people worldwide. About half the workforce is based in St. Louis; the remainder is split among their manufacturing plants. In the United States, the focus of sales is on the eastern seaboard, California, the Southeast, and the south-central states, which have the greatest concentration of customers. Outside the United States, PLE's sales include a European market, a growing South American market, and developing markets in the Pacific Rim and China. The market is cyclical, but the different products and regions balance some of this, with just less than 30% of total sales in the spring and summer (in the United States), about 25% in the fall, and about 20% in the winter. Annual sales are approximately $180 million. PLE has several key suppliers: Mitsitsiu, Inc., the sole source of all diesel engines; LANTO Axles, Inc., which provides tractor axles; Schorst Fabrication, which provides subassemblies; Cuberillo, Inc., a supplier of transmissions; and Specialty Machining, Inc., a supplier of precision machine parts. Elizabeth Burke has recently joined the PLE management team to oversee production operations. In reviewing data from the company's data warehouse / data mart, she noticed that defects received from suppliers have decreased (tab: Defects After Delivery). Upon investigation, she learned that in 2017, PLE experienced some quality problems due to an increasing number of defects in materials received from suppliers. The company instituted an initiative in August 2018 to work with suppliers to reduce these defects, to coordinate deliveries more closely, and to improve materials quality through reengineering supplier production policies. Elizabeth noted the program appeared to reduce 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 be further reduced soon.

Question 1. Consider the defects data from January 2017 through August 2018. Build a scatterplot of the defects over time. Fit (1) a simple linear regression model to the data, (2) a polynomial trendline of order 2, and (3) a polynomial trendline of order 3. Which model is the best fit for the data?

Question 2. Is the best fit model from question 1 a good predictor (at the time) of future defects? 1 This case is adapted from Evans, J. R. (2016). Business Analytics: Methods, Models, and Decisions (2nd ed.). Upper Saddle River: Pearson

Question 3. Is linear regression an appropriate model to use for making a prediction of defects between January 2017 and August 2018?

Question 4. Is the variable in your linear regression model significant?

Question 5. Do the residuals in your linear regression model suggest any potential issues with the model?

Question 6. Now consider all defects data, from January 2017 through December 2021. Build a scatterplot of the defects over time. Fit a simple linear regression model to the data and a polynomial trendline of order 2. Which model is the best fit for the data?

Question 7. Is the best fit model from question 6 a good predictor of future defects?

Question 8. When is the first month that PLE realized a clear drop in defects? Enter your answer as a month number; example: 89.

Question 9. Did that drop occur immediately after the supplier initiative was implemented in August 2018?

Question 10. Predict the number of defects for January 2022. Enter your solution as a whole number;

example: 42. 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 year of education and grade point average 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 current age have on retention. A sample of 40 field service engineers was selected to determine the influence of these variables on how long everyone stayed with the company. Data are compiled on the Employee Retention tab.

Question 11. Create a multiple linear regression model to predict the years an employee stays with PLE. Use all data given in the problem to make this prediction. Are all p-values significant the variables in the model?

Question 12. Considering regression best practices, which variables are in the final regression model that predicts the number of years an employee stays with PLE?

Question 13. Is the final regression model a good predictor?

Question 14. Use your final regression model with best practices to predict the number of years an employee stays with PLE. This employee is aged 45, had a college GPA of 3.15, and 16 years of education. Enter your answer as the number of whole years; example: 29.

Question 15. Now consider a multiple regression model with interaction of all variables (education X GPA), (education X age), (GPA X age). Is regression an appropriate analytic to use to make a prediction?

Question 16. Is the multiple linear regression model a good predictor?

Question 17. Select the variables that have significant p-values in this model. 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 lawnmower 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 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 lawnmower 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. 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. Elizabeth would like a better handle on this.

Question 18. Create a scatterplot of the units and production time. Does the production time increase, decrease, or stay about the same over time?

Question 19. Create a linear trendline model to predict production time. What is the R2 value for that model? Enter your answer as a decimal to three places; example: 3.871

Question 20. Is the linear trendline model a good predictor?

Question 21. Do your residuals in the model appear random?

Question 22. Use your linear trendline to predict the production time for unit 55. Enter your answer as a decimal to one place; example: 3.4

Question 23. Create a polynomial trendline of order 2 for the production time. Which model is a better predictor?