28 The U.S. government provides fuel economy (in miles per gallon) and other information about late model cars sold in the US. A linear regression model was used on the data to determine whether there was an associationbetween a car's engine displacement (Displacement) and fuel economy (MPG).Use the StatCrunch output to answer the following question.Simple linear regression results:Dependent Variable: MPGIndependent Variable: DisplacementMPG 37.49079-4.357743 DisplacementSample size: 35R (correlation coefficient) = -0.79692884R-sq-0.63509558Estimate of error standard deviation: 4.0040499Identify the slope, intercept, and association (positive or negative) and choose the correct statement below.The slope is 37.49, the intercept is -4.36, and the association is negative.The slope is 37.49, the intercept is -4.36, and the association is positive.The slope is -4.36, the intercept is 37.49, and the association is negative.The slope is -4.36, the intercept is 37.49, and the association is positive.

Concept: Slope represents the change in the dependent variable (I.e. Mpg) when you change the…

Answered: The U.S. government provides fuel…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 2ECP

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The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the data in Worksheet 2. Worksheet 2 Age of a Bus (years) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 Develop a scatter diagram with the age of a bus as the independent variable. Develop the estimated regression equation that can be used to predict the maintenance cost given the age of a bus. Determine the coefficient of determination, and interpret its meaning in this problem. At the 0.05 level of significance, is there evidence of a linear relationship between the age of a bus and the annual maintenance cost.
A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain. MPG HORSEPOWER WEIGHT 44 67 1,844 44 50 1,998 40 62 1,752 37 69 1,980 37 66 1,797 34 63 2,199 35 90 2,404 32 99 2,611 30 63 3,236 28 91 2,606 26 94 2,580 26 88 2,507 25 124 2,922 22 97 2,434 20 114 3,248 21 102 2,812 18 114 3,382 18 142 3,197 16 153 4,380 16 139 4,036
A mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 What is the predicted area of a kitchen with a height of 96 inches and 10 cabinets? Report your answer to 1 decimal place. square feet
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 10 Question 10 This is not a form; we suggest that you use the browse mode and read all parts of the question carefully. Which of the following is the correct interpretation of the coefficient for Cabinets? For a kitchen with a given ceiling height, the average number of cabinets…
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example? The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches.…
The regional transit authority for a major metropolitan area wants to determine whetherthere is a relationship between the age of a bus and the annual maintenance cost. A sampleof ten buses resulted in the following data: a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between age of a bus and the annual maintenance cost?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance cost given the age of the bus. What is the estimated regressionmodel?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of annual maintenance cost does themodel you estimated in part b explain?e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?
A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop1 54 17 03 32 52 45 15 21 86 2 The estimated regression equation and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)Se=1.229787 Suppose a new employee has had 1 hour of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.
A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years of Experience Annual Sales ($1000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136 Develop a scatter diagram for these data with years of experience as the independent variable. Develop an estimated regression equation that can be used to predict annual sales given the years of experience. Use the estimated regression equation to predict annual sales for a salesperson with 9 years of experience.
Suppose a commercial developer in Vereeniging consider to purchase a group of small office buildings in an established business district. He uses multiple linear regression analysis, which was based on a sample of 35 office buildings, to estimate the value of an office building in a given area based on the following variables. Y = Assessed value of the office building (in Rand) X1= Floor space in square meters X2= Number of offices X3= Age of the office building in years Answer the questions that follow by typing only the letter of the correct option (A, B, C, D or E) in the answer spaces provided. Variablesy: Valuex1: Floor Spacex2: Officesx3: Age Model Fitting StatisticsR^2 = 0.9752Adj R^2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates Error of Beta Estimates Error of b t Statistic Prob > |t|Intcpt…

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