The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x₁) and newspaper advertising (x₂). The estimated regression equation wasŷ = 83.5+ 2.21x₁ + 1.80x₂.The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495.(a) Compute and interpret R² and R2. (Round your answers to three decimal places.)The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation isvariable that can be explained by the estimated multiple regression equation is(b) When television advertising was the only independent variable, R² = 0.653 and R2 = 0.595. Do you prefer the multiple regression results? Explain.Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used.. Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 82.4 + 2.23x1 + 1.40x2. The computer solution, based on a sample of eight weeks, provided SST = 25.5 and SSR = 23.495.(Note: SST = SS yy ) (a)Compute and interpret R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . (b)When television advertising was the only independent variable, R2 = 0.653 and Ra2 = 0.595. Is the multiple regression model more preferable over the simple regression model? Explain. Multiple…
The police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-1.145 b=20.742 r?=0.508369 r=-0.713 Use this to predict the number of situps a person who watches 2.5 hours of TV can do (to one decimal place)
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-1.226 b=33.622 r²-0.4489 r=-0.67 Use this to predict the number of situps a person who watches 3 hours of TV can do (to one decimal place)
A regression analysis was performed to determine if there is a relationship between hours of TV watched per day (xx) and number of sit ups a person can do (yy). The results of the regression were: y=ax+b a=-1.152 b=30.418 r2=0.703921 r=-0.839 1. Use this to predict the number of sit ups a person who watches 2.5 hours of TV can do, and please round your answer to a whole number
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). The equation CITY = -3.14 +0.818HWY was previously determined to be the best for predicting city fuel consumption. A car weighs 2760 lb, it has an engine displacement of 2.2 L, and its highway fuel consumption is 34 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Click the icon to view the table of regression equations. The best predicted value of the city fuel consumption is (Type an integer or a decimal. Do not round.) Regression Table Predictor (x) Variables P-Value R² Adjusted R² WT/DISP/HWY WT/DISP WT/HWY DISP/HWY 0.000 0.943 0.000 0.747 0.000 0.941…
The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last 7 years. Construct and interpret a 98% prediction interval for the amount of oil imported by the country and the amount of oil produced by the country is 5,483 thousand barrels per day. The equation of the regression line is y = -1.194x + 16,234.906
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The table shows the number of goals allowed and the total points earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is ŷ= -0.556x+217.766. Use the data to answer the following questions. (a) Find the coefficient of determination, 12, and interpret the result. (b) Find the standard error of the estimate, Se, and interpret the result. 213 213 223 226 259 266 281 202 210 205 226 207 259 239 D Goals Allowed, x Points, y 109 109 102 91 88 80 52 105 107 98 95 85 68 66 (a)² = (Round to three decimal places as needed.) Interpret the coefficient of determination. Select the correct choice below and fill in the answer box to complete your choice. (Round to one decimal place as needed.) OA. About OB. About (b) Se = % of the variation in points earned can be explained by the relationship between number of goals allowed and points earned. The remaining variation is unexplained. % of the…
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-1.091 b=30.228 r2=0.698896 r=-0.836 Use this to predict the number of situps a person who watches 3.5 hours of TV can do (to one decimal place)
A regression analysis was performed to determine if there is a relationship between hours of TV watched per day (xx) and number of sit ups a person can do (yy). The results of the regression were: y=ax+b a=-1.013 b=27.906 r2=0.498436 r=-0.706 Use this to predict the number of sit ups a person who watches 12 hours of TV can do, and please round your answer to a whole number.
The table shows the number of goals allowed and the total polints earned (2 points for a win, and 1 point for an overtime or shootout loss) by 14 ice hockey teams over the course of a season. The equation of the regression line is y= -0.573x+220.523. Use the data to answer the following questions. (a) Find the coefficient of determination, , and interpret the result. (b) Find the standard error of the estimate, s and interpret the result. Goals Allowed, x Polnts, y 209 205 220 226 261 266 275 201 214 204 224 201 263 244 D 111 108 100 97 84 82 44 107 105 95 92 86 67 69 (0) ? =D (Round to three decimal places as needed.) Interpret the coefficient of determination. Select the correct choice below and fill in the answer box to complete your choice. (Round to one decimal place as needed.) O A. About % of the variation in number of goals allowed can be explained by the relationship between number of goals allowed and points eamed. The remaining variation is unexplained. O B. About % of the…

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