The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x 1) and newspaper advertising (x 2). The estimated regression equation was ŷ = 87.2 + 1.39 x 1 + 0.54 x 2 Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 2.5 91 2 2 96 5 2.5 93 2.5 3.5 95 4 4.3 94 4.5 2.3 94 3.5 4.2 94 4 2.5 The computer solution provided SST = 23.5 and SSR = 22.437. Compute R 2 and R a 2 (to 3 decimals). R 2   R a 2

Data were collected on monthly sales revenues​ (in $1,000s) and monthly advertising expenditures​ ($100s) for a sample of drug stores. The regression line relating revenues​ (Y) to advertising expenditure​ (X) is estimated to be y=−48.3+9.00x. What is the correct interpretation of the​ slope?

The number of megapixels in a digital camera is one of the most important factors in determining picture quality. But, do digital cameras with more megapixels cost more? The following data show the number of megapixels and the price ($) for 10 digital cameras(Consumer Reports, March 2009). Use these data to develop an estimated regression equation that can be used to predict the price of a digital camera given the number of megapixels. Brand and Model Megapixels Price (S) Canon PowerShot SD1100 IS Casio Exilim Card EX-510 8 180 200 230 10 Sony Cyber-shot DSC-T70 Pentax Optio M50 Canon PowerShot G10 120 470 15 8 Canon PowerShot A590 IS Canon PowerShot El 140 180 10 12 Fujifilm FinePix FOOFD Sony Cyber-shot DSC-W170 Canon PowerShot A470 310 10 250 110

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 following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is  ŷ = 23.462 + 0.315x,  where x = price ($) and y = overall score. Brand Price ($) Score A 180 74 B 150 73 C 95 59 D 70 58 E 70 42 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST=SSR=SSE= (b) Compute the coefficient of determination  r2.  (Round your answer to three decimal places.) r2  =  Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of…

The table below shows the average weekly wages​ (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is​ $878.The equation of the regression line is y=1.342x+55.816. Wages [state]- 712, 746, 786, 803, 841, 879, 918, 926, 954, 979 Wages [federal]- 1,024, 1,048, 1,098, 1,135, 1,195, 1,240, 1,270, 1,299, 1,340, 1,376 Construct and interpret a 98​% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $878. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as​ needed.)     PICK THE CORRECT ANSWER [A] We can be 98​% confident that when the average weekly wages of state government employees is $878​, the average weekly wages of…

The following data show the brand, price (S), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.522 + 0.335x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 78 B 150 73 95 63 70 58 E 70 38 35 26 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination rt. (Round your answer to three decimal places.) 12 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a small proportion of the variability in y…

The accompanying data are the caloric contents and the sugar contents​ (in grams) of 11 ​high-fiber breakfast cereals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the x-value is not meaningful to predict the value of​ y, explain why not.  Calories, x         Sugar, y 140                      6 200                     10 160                      6 160                      9 170                     10 180                     16 190                     13 210                     18 190                     19 170                     10 170                     10   The equation of the regression line is ŷ =  ______ x + ______ ​(Round the slope to three decimal places as needed. Round the​ y-intercept to two decimal places as​ needed.)      (a) x = 150 cal,  ​ (b) x = 90 cal,   (c) x = 175 cal,   ​(d) x = 208 cal…

The slope of a regression line tells you how much or little a change in your dependent variable impacts your independent variable. O TrueO False

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.525 + 0.325x, where x = price ($) and y overall score. %3D Brand Price ($) Score 180 78 B. 150 71 C 95 59 70 54 E 70 40 35 28 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST SSR %3D SSE = (b) Compute the coefficient of determination . (Round your answer to three decimal places.) 1 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a large proportion of the variability in y…