Management proposed the following regression model to predict sales at a fast-food outlet.y = Bo + B,x1 + B2X2 + B3X3 + EwhereX1 = number of competitors within one mileX2 = population within one mile (1,000s)J1 if drive-up window present0 otherwisey = sales ($1,000s).X3 =The following estimated regression equation was developed after 20 outlets were surveyed.ŷ = 10.5 – 4.2x, + 6.8x2 + 15.9x3(a) What is the expected amount of sales (in dollars) attributable to the drive-up window?$(b) Predict sales (in dollars) for a store with three competitors within one mile, a population of 8,000 within one mile, and a drive-up window.24(c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and no drive-up window.$4

Answered: Management proposed the following…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Does Table 2 represent a linear function? If so, finda linear equation that models the data.
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A real estate company wants to study the relationship between house sales prices and some important predictors of sales prices. Based on data from recently sold homes in the space, the following variables are used in a multiple regression model. y = sales price (in thousands of dollars) x₁ = total floor area (in square feet) x₂ = number of bedrooms x3 distance to nearest high school (in miles) = The estimated model is as follows. =76+0.098x₁ +16x₂ - 8x3 Answer the questions below for the interpretation of the coefficient of X₂ in this model. (a) Holding the other variables fixed, what is the average change in sales price for each additional bedroom in a house? dollars (b) Is this change an increase or a decrease? O increase O decrease X
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. ..... a. Construct a scatter plot. Choose the correct graph below. A. Ов. С. D. ACost ($) 90- ACost ($) 90- ACost ($) 90- ACost ($) 90- 0- 0- 90 90 90 90 Rating Rating Rating Rating b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b, and b,. bo = and b, (Round to two decimal places as needed.) c. Interpret the meaning of the Y-intercept, bo, and the slope, b,. Choose the correct answer below. O A.…
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. a. Construct a scatter plot. Choose the correct graph below. O A. Ов. OC. OD. ACost ($) 90- Q A Cost ($) 904 A Cost ($) 90- ACost ($) 90- 0- 0- 0- 0- 90 Rating 90 Rating 90 90 Rating Rating Summated ratings and cost per person b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and b,. bo =D and b, =O (Round to two decimal places as needed.) Summated Rating Cost ($ per person)|9 c. Interpret the…
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. Click the icon to view the table of summated ratings and cost per person. a. Construct a scatter plot. Choose the correct graph below. O A. 90+ 0 0 Cost ($) The M Rating 90 Q O B. A Cost (5) 90+ 0 H +4 Alpe Rating 90 Q b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and b₁. bo= and b₁ = (Round to two decimal places as needed.) C O C. 90+ 0- Cost (S) HA Rating 90 Q Summated Ratings and Cost Per Person Summated Rating Cost ($ per person) 40 48 60 61 42 40 43 55 67 69…
A real estate company wants to study the relationship between house sales prices and some important predictors of sales prices. Based on data from recently sold homes in the space, the following variables are used in a multiple regression model. y sales price (in thousands of dollars) x₁ = total floor area (in square feet) X₂= number of bedrooms x3² distance to nearest high school (in miles) The estimated model is as follows. y=121 +0.083x₁ +23x₂ - 4x3 Answer the questions below for the interpretation of the coefficient of x₁ in this model. (a) Holding the other variables fixed, what is the average change in sales price for each 100-square-foot increase in floor area? dollars (b) Is this change an increase or a decrease? increase decrease X Ś
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 ($) for 10 digital cameras(Consumer Reports, March 2009). The Kodak Easy Share Z1012 IS digital camera has 10 megapixels. Predict the price of this camera using the estimated regression equation developed. Brand and Model Megapixels Price (S) Canon PowerShot SD1100 IS Casio Exilim Card EX-510 180 200 230 8 10 Sony Cyber-shot DSC-T70 Pentax Optio M50 Canon PowerShot G10 Canon PowerShot A590 IS Canon PowerShot El 8 120 470 15 140 180 310 250 10 Fujifilm FinePix FO0FD Sony Cyber-shot DSC-W170 Canon PowerShot A470 12 10 110
After interviewing salespersons at Harley Davidson dealerships, a researcher has created a linear regression line to explain the relationship between a Harley Davidson motorcycle's age (x) and price (y). The regression has an = 87.7%. Write a sentence summarizing what says about this regression. The age of the motorcycle explains 12.3% of the variation in price. The age of the motorcycle explains 9.36% of the variation in price. The age of the motorcycle explains 87.7% of the variation in price. The price of the motorcycle explains 12.3% of the variation in age. The price of the motorcycle explains 87.7% of the variation in age.
The number of megapixels in a digital camera is one of the most important factors in determining picture quality. But, do digital cameras with more megapixels cost more? The following data show the number of megapixels and the price ($) for 10 digital cameras(Consumer Reports, March 2009). Would you feel comfortable using the estimated regression equation developed to predict the price of a digital camera given the number of megapixels? Explain. Brand and Model Megapixels Price (S) Canon PowerShot SD1100 IS Casio Exilim Card EX-510 180 200 230 8 10 Sony Cyber-shot DSC-170 Pentax Optio M50 Canon PowerShot Gl10 8 120 470 15 Canon PowerShot A590 IS 8 140 Canon PowerShot El Fujifilm FinePix FOOFD Sony Cyber-shot DSC-W170 Canon PowerShot A470 10 12 180 310 10 250 110
Bowling Corporation wants to know how closely its current cost driver is correlated with its monthly operating costs. The managerial accountant runs a regression analysis using a statistical software program and produces the following data: Intercept Coefficient = 12,200,567 X Variable 1 Coefficient = 95.65 R-square= 0.8574 What is the Bowling Corporation's monthly cost equation? OA. y $95.65x + $12,200,567 OB. y $95.65x + $8.574 O c. y = $0.8574x + $12,200,567 O D. y = $12,200,567x + $8,574 ---

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