Suppose two variables are positively related. Which of the following regression equations might describe this relationship? Y = 4.1 Y = 1.45 +4.1X Y = 3.2 - 2.4X Y = -0.2X+3.2
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- The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 21.656 + 0.333x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 73 95 61 70 54 E 70 42 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination r. (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 did not provide 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 provided a good fit as a small proportion of the variability in y…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 Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 91 3 2 95 5 2.5 93 3.5 2.5 96 4 4.3 94 4.5 2.3 95 3.5 4.2 95 4 3.5 ŷ = 82.5 + 2.01 x 1 + 1.26 x 2The computer solution provided SST = 24 and SSR = 22.876. Compute R 2 and R a 2 (to 3 decimals). R 2 R a 2 When television advertising was the only independent variable, R 2 = 0.551 and R a 2 = 0.476. Are the multiple regression analysis results preferable?The accompanying data are the shoe sizes and heights (in inches) of 14 men. 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. (a) x=11.5 (b) x=8.0 (c) x=15.5 (d) x= Shoe Size, x Height, y8.5 66.09.0 69.09.0 67.59.5 70.510.0 70.510.0 72.010.5 71.510.5 70.011.0 71.011.0 71.511.0 73.012.0 73.012.0 74.012.5 73.5 The equation of the regression line is y= ____x +____
- 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?Imagine Daenerys Targaryen as a researcher concerned with the dragon species. The people of Westeros believed that dragons were decreasing in size due to captivity. Dragon size was normally measured as wingspan (meters) and captivity was normally measured in years. Daenerys used archival data and determined that the relationship between these two variables could be explained using the following regression equation: y-predicted = 453 - 2.5xInterpret this equation (i.e. What is its purpose? What is the intercept? What is the slope? What does it mean for dragons in Westeros?).Draw the regression line for the following equation: Y = -3 + (1) X Show your calculation for a low and high value on the predictor value.
- Researchers used the simple linear regression model to study the relationship between social media screen time during a week and end-of-week quiz results. As one of the researchers, find the predicted quiz score if a student spends 18.46 hours during the next week using social media. Use the data in the table below to build the estimated regression equation and then use this equation to find the predicted quiz score: Social media weekly time, hours 14.5 3.7 30.4 34.23 2.7 16.8 13.6 4,7 20,6 4.9 Round your answer to 2 decimals. Less I Quiz results, out of 100 76.8 98.45 57.6 45.5 74.78 75.7 93.67 57.8 35.7 94.8The 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 $888 the equation of the regression line is y= 1.453x-47.386. Wages(state), X | 739|760|784|822|898|921|937|954|965| Wages (federal), Y |1,036|1,054|1,105|1,136|1,192|1,253|1,266|1,327|1,400|The following data show the brand, price (S), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.522 + 0.335x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 78 B 150 73 95 63 70 58 E 70 38 35 26 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST = SSR = SSE = (b) Compute the coefficient of determination rt. (Round your answer to three decimal places.) 12 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a small proportion of the variability in y…
- A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents attendance (in thousands) and ŷ is the predicted number of wins. Which statement best describes the meaning of the slope of the regression line? For each increase in attendance by 1,000, the predicted number of wins increases by 4.9. For each increase in attendance by 1,000, the predicted number of wins increases by 15.2. For each increase in the number of wins by 1, the predicted attendance increases by 4,900. For each increase in the number of wins by 1, the predicted attendance increases by 15,200.The following data show the brand, price ($), 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…Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snel| "SA" (Sports Application) rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets (SoloRacer website). Helmet Weight (oz) Price ($) Pyrotect Pro Airflow 64 241 Pyrotect Pro Airflow Graphics 64 276 RCi Full Face 64 202 RaceQuip RidgeLine 64 197 HJC AR-10 58 291 HJC Si-12 47 708 HJC HX-10 49 910 Impact Racing Super Sport 59 331 Zamp FSA-1 66 197 Zamp RZ-2 58 292 Zamp RZ-2…