State University administrators believe their freshman applica-tions are influenced by two variables: tuition and the size of theapplicant pool of eligible high school seniors in the state. Thefollowing data for an eight-year period show the tuition rates(per semester) and the sizes of the applicant pool for each year:a. Using Excel, develop the multiple regression equationfor these data.b. What is the coefficient of determination for thisregression equation?c. Determine the forecast for freshman applicants fora tuition rate of $1500 per semester with a pool ofapplicants of 60,000. Tuition ($) Applicant Pool Applicants900 76,200 11,0601250 78,050 10,9001375 67,420 8,6701400 70,390 9,0501550 62,550 7,4001625 59,230 7,1001750 57,900 6,300

State University administrators believe their freshman applica-tions are influenced by two variables: tuition and the size of theapplicant pool of eligible high school seniors in the state. Thefollowing data for an eight-year period show the tuition rates(per semester) and the sizes of the applicant pool for each year:a. Using Excel, develop the multiple regression equationfor these data.b. What is the coefficient of determination for thisregression equation?c. Determine the forecast for freshman applicants fora tuition rate of $1500 per semester with a pool ofapplicants of 60,000. Tuition ($) Applicant Pool Applicants900 76,200 11,0601250 78,050 10,9001375 67,420 8,6701400 70,390 9,0501550 62,550 7,4001625 59,230 7,1001750 57,900 6,300

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.4: Multiple Regression Models

Problem 16P: Suppose that a regional express delivery service company wants to estimate the cost of shipping a...

See similar textbooks

Similar questions

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?
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.
Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for 16 electric utility stocks are provided in the file P13_15.xlsx. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
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.
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.
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_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. 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?
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?
The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers). a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?
Cadbury Schweppes owns and operates a chain of 12 vegetable protein "hamburger" outlets in northern Louisiana. Sales figures and advertising expenses for the stores are provided in the table below. Sales are given in millions of dollars; advertising expenses are in tens of thousands of dollars. Calculate a regression line for the data. What is your forecast of sales for a store with advertising spending of R240,000? R300,000? Store 1 2 3 4 5 6 7 8 9 10 11 12Advertising 14 11 15 16 24 28 22 21 26 43 34 9Sales 6 3 5 5 15 18 17 12 15 20 14 5
Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Mark has collected the data shown in the following table: Demand for Guitars 3 6 7 5 10 7 Maroon 5 TV Appearances 3 4 7 6 8 5 Graph these data to see whether a linear equation might describe the relationship between the group’s television shows and guitar sales. Use the least-squares regression method to derive a forecasting equation. Use the least-squares regression method to derive a forecasting equation. What is your estimate for guitar sales if Maroon 5 performed on TV nine times last month? Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average and a four-period moving average for weeks 5, 6, and 7. Compute the MAD for both forecasting methods. Which model is more…