a) Use the model to predict the selling price of a house that is 1,860 square feet. b) An 1,860-square-foot house recently sold for $95,000. Explain why this is not what the model predicted.
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- 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_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 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.
- eBook Problem 6-23 (Algorithmic) The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study. Year 1 2 3 A 4 5 5 6 6 7 2 A 4 9 10 11 12 13 14 15 Percentage of Adults Who Exercise 30 or more minutes at least three times per week 41.2 45.1 47.3 45.6 46.6 44.5 47.8 50 48.1 49.1 50.1 52.1 50.8 54.6 52.4Make a 15-year simple linear regression forecast. Example: Railroad Products Co. RPC Sales Car Loadings Year ($millions) (millions) 1 9.5 120 2 11.0 135 3 12.0 130 4 12.5 150 5 14.0 170 6 16.0 190 7 18.0 220For the E-Commerce Retail Sales (Million$) data given in the table below, provide estimates from the 1st Quarter (Q1) of 2016 to the 3rd Quarter (Q3) of 2017 by using two models: 1) Single Exponential Smoothing with α=0.3 2) Moving Average with k=2. Calculate MAPE for each model. Quarter Year Actual Q1 2016 86802 Q2 2016 92004 Q3 2016 93795 Q4 2016 124651 Q1 2017 99491 Q2 2017 106590 Q3 2017 108291 Compare two models above (Single Exponential Smoothing and Moving Average) based on their accuracies. Which forecasting method appears to be better? Using the model you choose, provide forecast for the 4th Quarter (Q4) of 2017. Assuming that this model is overestimating, find the actual value of the Q4 of 2017 based on MAPE value. Some residual graphs from the first forecast model (including wider range of E-Commerce Retail Sales data) are given below. What do these graphs tell about the model? Explain each graph.
- Regression and Utility Rates; Sustainability For several years, many utilities haveemployed regression analysis to forecast monthly utility usage by residential customers usingweather forecasts, the number of holidays, the number of days in the month, and other factors.For example, the Connecticut Department of Public Utility Control (CDPUC) has determinedthat regression, properly used, can accurately predict natural gas usage. Most public gas utilities serving Connecticut have reported levels of accuracy from 4% to 10% using regression.One company, Dominion Natural Gas Company of Ohio, uses this approach not to forecast, butto explain to customers why their natural gas bills have gone up or down compared to the priormonth and to the same month of the prior year. The bill shows total MCF (thousand cubic feetof natural gas) used by the customer for that month and why the total MCF usage has changed,based on three factors:1. Change in temperature. Each degree increase in temperature…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 6.7b. 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.Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks? Week 1 2 3 4 5 Sales 150 157 162 166 177