18 Oct 2 review simple linear regression

The manager of the Salem police department motor poolwants to develop a forecast model for annual maintenanceon police cars based on mileage in the past year and age ofthe cars. The following data have been collected for eightdifferent cars: a. Using Excel develop a multiple regression equationfor these data.b. What is the coefficient of determination for thisregression equation?c. Forecast the annual maintenance cost for a police carthat is four years old and will be driven 10,000 miles inone year.

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 52.4

Q1: Income at the architectural firm Spraggins and Yunes for the period February to July was as follows: Month February March April May June July 72.8 Income (in $ 70.0 thousand) 68.5 64.5 71.7 71.3 Use trend-adjusted exponential smoothing to forecast the firm's August income. Assume that the initial forecast average for February is $65,000 and the initial trend adjustment is 0. The smoothing constants selected are a = .1 and B =.2.

The number of internal disk drives (in millions) made at a plant in Taiwan during the past 5 years follows:                           Year              Disk Drives                                1                    142                                2                     156                               3                       184                                 4                     204                                5                      210 a) Using simple linear regression the forecast for the number of disk drives to be made next year= 234.4  disk drives b) The mean squared error when using simple linear regression = 24.64 drives2 c) The mean absolute percentage error (mape) when using simple linear regression= [___]% (round your response to 1 decimal place)

The following data describes weekly gross revenue ($1000s), television advertising expenditures ($1000s), and newspaper advertising expenditures ($1000s) for Showtime Movie Theaters. × Weekly Gross + Revenue ($1000s) 99 90 95 92 95 94 94 94 a. Find an estimated regression equation relating weekly gross revenue to television advertising expenditures and newspaper advertising expenditures (to 2 decimals). 2.84 Television Advertising ($1000s) 5.0 2.0 4.0 2.5 3.0 3.5 2.5 3.0 Revenue = 81.73 1.29 News Adv TV Adv + b. Choose the correct plot of the standardized residuals against ĝ. Newspaper Advertising ($1000s) 1.5 2.0 1.5 2.5 3.3 2.3 4.2 2.5

Regression analysis. The owner of a small hardware store has noted a sales pattern for window locks  that seems to parallel the number of break-ins reported each week in the newspaper. The data are: Sales: 46 18 20 22 27 34 14 37 30Break-ins: 9 3 3 5 4 7 2 6 4a. Plot the data to determine which type of equation, linear or nonlinear, is appropriate.b. Obtain a regression equation for the data.c. Estimate average sales when the number of break-ins is five.

A manufacturing firm has developed a skills test, the scores from which can be used to predict workers’ production rating factors. Data on the test scores of various workers and their subsequent production ratings are shown.a. Using POM for Windows’ least squares-linear regression module, develop a relationship to forecast production ratings from test scores.b. If a worker’s test score was 80, what would be your forecast of the worker’s production rating?c. Comment on the strength of the relationship between the test scores and production ratings.

Restaurant Student Population Quarterly Sales 1 2 58 2 6 105 3 8 88 4 8 118 5 12 117 6 16 137 For the data above, what would be the predicted quarterly sales for a restaurant with a student population of 15 (using linear regression)?

Ayamas Food Corporation Sdn. Bhd. company needs to estimate its sales for next year. The most recent six years of revenue data for the company's most popular line of Ayamas are given below: Year Sales revenue (Millions of dollars) 1 10 2 13 3 15 4 16 5 18 6 20 a) Use simple linear regression to forecast the sales revenue for the next THREE (3) years. (14 Marks) b) Determine the correlation coefficient for the data and interpret its meaning. (4 Marks) c) Determine the coefficient of determination for the data and interpret its meaning. (2 Marks)

The number of internal disk drives (in millions) made at a plant in Taiwan during the past 5 years follows: Year Disk Drives 1 138 2 156 3 184 4 202 220 a) Using simple linear regression, the forecast for the number of disk drives to be made next year = 211 disk drives (round your response to one decimal place). b) The mean squared error (MSE) when using simple linear regression = drives- (round your response to one decimal place). c) The mean absolute percentage error (MAPE) when using simple linear regression = % (round your response to one decimal %3D place).

(8 points) Infoworks is a large computer discount store that sells computers and ancillary equipment and software in the town where a State University is located. Infoworks has collected historical data on computer sales and printer sales for the past 10 years, as follows:       Develop a linear regression model relating printer sales to computer sales in order to forecast printer demand in year 11 if 1,300 computers are sold.   Develop a moving-average model with n = 3 to forecast printer demand in year 11   Develop an exponential smoothing model with α = .30 to forecast printer demand in year 11. Compare your result in a, b, c. Which model would you choose and why?

Movieflix, an online movie streaming service that offers a wide variety of award-winning TV shows, movies, animes, and documentaries, would like to determine the mathematical trend of memberships in order to project future needs. Year                              2013 2014 2015 2016 2017 2018 2019 2020 2021Membership (000s)   17      16      16     21     20      20     23      25      24    1. Provide an example of qualitative forecasting and explain the shortcomings.

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Problem 3

The H.W. Grant Corporation used regression analysis to predict the annual cost of indirect materials. The results were as follows: Indirect Materials Cost Explained by Units Produced Constant $15,675 Standard error of Y estimate $3,500 0.7776 Number of observations 16 X coefficient(s) 10.25 Standard error of coefficient(s) 2.195 What is the cost estimation equation? O A. Y= $12,175 + $10.25X O B. Y= $3,500 + $7.97X O C. Y= $19,175 + $4.67X O D. Y= $15,675 + $10.25X

Sales of​ Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years​ (see table​ below). Using exponential smoothing with a smoothing constant ​(α​) of 0.30 and a starting forecast of 415.00​, the following sales forecast has been​ developed:                                                                                     Year Sales Forecasted Sales 2005 455 415.00 2006 502 427.00 2007 518 449.50 2008 563 470.05 2009 584 497.94 Part 2 The MAD for a forecast developed using exponential smoothing with α ​= 0.30 is enter your response here sales ​(round your response to two decimal​ places). Part 3 Forecasted sales for years 2006 through 2010 using exponential smoothing with α ​= 0.60 and a starting forecast of 415.00 are ​(round your responses to two decimal ​places)​:   Year 2005 2006 2007 2008 2009 2010 Forecasted Sales 415.00 enter your response here enter…