Lovely Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store man- ager estimates a probable six-week lag between fertilizer sales and mower sales. The pertinent data are: Period 1 234567 2 3 4 5 7 Fertilizer Sales (tons) 1.6 1.3 1.8 2.0 2.2 1.6 1.5 Number of Mowers Sold (six-week lag) 10 8 11 12 12 9 8 Period 8 9 10 11 12 13 14 Fertilizer Sales (tons) 1.3 1.7 1.2 1.9 1.4 1.7 1.6 Number of Mowers Sold (six-week lag) 7 10 6 11 8 10 9 a. Determine the correlation between the two variables. Does it appear that a relationship between these variables will yield good predictions? Explain. b. Obtain a linear regression line for the data. c. Predict expected lawn mower sales for the first week in August, given fertilizer sales six weeks earlier of 2 tons.

Lovely Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store man- ager estimates a probable six-week lag between fertilizer sales and mower sales. The pertinent data are: Period 1 234567 2 3 4 5 7 Fertilizer Sales (tons) 1.6 1.3 1.8 2.0 2.2 1.6 1.5 Number of Mowers Sold (six-week lag) 10 8 11 12 12 9 8 Period 8 9 10 11 12 13 14 Fertilizer Sales (tons) 1.3 1.7 1.2 1.9 1.4 1.7 1.6 Number of Mowers Sold (six-week lag) 7 10 6 11 8 10 9 a. Determine the correlation between the two variables. Does it appear that a relationship between these variables will yield good predictions? Explain. b. Obtain a linear regression line for the data. c. Predict expected lawn mower sales for the first week in August, given fertilizer sales six weeks earlier of 2 tons.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.3: Simple Regression Models

Problem 6P: Do the sales prices of houses in a given community vary systematically with their sizes (as measured...

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The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?
The file P13_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least the near future. a. Explain briefly whether the plot of the series visually supports the companys suspicion. b. By what percentage are sales increasing each month? c. What is the MAPE for the forecast model in part b? In words, what does it measure? Considering its magnitude, does the model seem to be doing a good job? d. In words, how does the model make forecasts for future months? Specifically, given the forecast value for the last month in the data set, what simple arithmetic could you use to obtain forecasts for the next few months?
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.
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The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.
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The file P13_25.xlsx contains the quarterly numbers of applications for home mortgage loans at a branch office of Northern Central Bank. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b? Is it guaranteed to produce better forecasts for the future?
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