Dr. Lillian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leavetheir homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It alsoindicates what the robbery rate was in New Orleans during the same year:YearNumber of PatientsRobbery Rate per1,000 Population12343733414158.3 60.6 73.0 75.754281.1The simple linear regression equation that shows the best relationship between the number of patients and year is(round your responses to three decimal places):ŷ=+xAwhere y = Dependent Variable and x = Independent Variable.678910565853596089.0 101.5 94.8 104.1 117.2 Café Michigan's manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price beingcharged. Based on historical observations, Gary has gathered the following data, which show the numbers of thesecoffees sold over six different price values:Price$2.70$3.50$2.10$4.10$3.10$4.05Number Sold765515990245320480Using simple linear regression and given that the price per cup is $1.85, the forecasted demand for mocha latte coffeeswill be cups (enter your response rounded to one decimal place).

Dr. Lillian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year: Year Number of Patients Robbery Rate per 1,000 Population 1 2 3 4 5 6 7 8 9 10 37 33 41 41 42 56 58 53 59 60 58.3 60.6 73.0 75.7 81.1 89.0 101.5 94.8 104.1 117.2 The simple linear regression equation that shows the best relationship between the number of patients and year is (round your responses to three decimal places): ŷ=+x where y = Dependent Variable and x = Independent Variable.

Dr. Lillian Fok, a New Orleans psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Fok has seen each year for the past 10 years. It also indicates what the robbery rate was in New Orleans during the same year: Year Number of Patients Robbery Rate per 1,000 Population 1 2 3 4 5 6 7 8 9 10 37 33 41 41 42 56 58 53 59 60 58.3 60.6 73.0 75.7 81.1 89.0 101.5 94.8 104.1 117.2 The simple linear regression equation that shows the best relationship between the number of patients and year is (round your responses to three decimal places): ŷ=+x where y = Dependent Variable and x = Independent Variable.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.6: Moving Averages Models

Problem 22P: The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six...

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Under what conditions might a firm use multiple forecasting methods?
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
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?
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_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?
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.
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?
3. Quarterly sales of a car dealer exhibit an almost constant mean over time, but sales fluctuate depending on the quarter of the year (exhibits seasonality). Quarter Q1 - Spring Q2 - Summer Q3 - Fall Q4 - Winter Mean Year 1 32 74 53 22 45.25 Year 2 30 71 63 15 44.75 Year 3 35 83 45 19 45.5 (a) Using three years' worth of quarterly data that is provided, develop a set of seasonal factors that could be used to forecast car sales (b) Forecast car sales in each of the four quarters (Q1-Q4) of the following year (Year 4), using these seasonal factors.
Café Michigan's manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the numbers of these coffees sold over six different price values: Price Number Sold $2.50 760 $3.40 515 $2.10 980 $4.20 245 $3.00 325 $4.00 475 Using simple linear regression and given that the price per cup is $1.75, the forecasted demand for mocha latte coffees will be _____?_____ cups (enter your response rounded to one decimal place).
The number of patients coming to the Healthy Start Maternity clinic has been increasing steadily over the past eight months. You are provided with some historical data as follows:Month Clinic attendance (in thousands) 1 3.42 3.93 4.54 5.05 5.86 5.97 6.58 6.7a. Identify and give a brief explanation of the:-i. Dependent variableii. Independent variable b. Use simple linear regression to forecast annual demand for months 9 and 10 by using the tabular method to:-i. Derive the values for the intercept and slope. ii. Derive the linear regression equation.iii. Plot the linear regression line. iv. Develop a forecast of the clinic attendance for months 9 and 10.
The number of patients coming to the Healthy Start Maternity clinic has been increasing steadilyover the past eight months. You are provided with some historical data as follows: Month Clinic attendance (in thousands)1 3.42 3.93 4.54 5.05 5.86 5.97 6.58 6.7 a. Identify and give a brief explanation of the:i. Dependent variableii. Independent variable b. Use simple linear regression to forecast annual demand for months 9 and 10 by using thetabular method to:i. Derive the values for the intercept and slope. ii. Derive the linear regression equation. iii. Plot the linear regression line. iv. Develop a forecast of the clinic attendance for months 9 and 10.
A pharmacist has been monitoring sales of a certain over-the-counter pain reliever. Daily sales duringthe last 15 days wereDay: 1 2 3 4 5 6 7 8 9Number sold: 36 38 42 44 48 49 50 49 52Day: 10 11 12 13 14 15Number sold: 48 52 55 54 56 57a. Using linear trend equation method, predict future sales from the given data.b. If you learn that on some days the store ran out of the specific pain reliever, would that knowledge cause you any concern? Explain.