We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 12091209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) What does the numerical value of the slope tell you? On average, highway mileage decreases by 0.9930.993 mpg for each additional mpg in city mileage. On average, highway mileage increases by 0.9930.993 mpg for each additional mpg in city mileage. For every 7.9037.903 mpg in city gas mileage, highway gas mileage increases about 0.9930.993 mpg. Highway gas mileage increases with city gas mileage by 7.9037.903 mpg for each additional mpg in city mileage. On average, highway mileage increases by 7.9037.903 mpg for each additional mpg in city mileage. (b) What is the intercept? (Enter your answer rounded to three decimal places.) intercept: mpg Why is the value of the intercept not statistically meaningful? The value of the intercept represents the predicted highway mileage for city gas mileage of 00 mpg, and such a car does not exist. The value of the intercept represents the predicted highway mileage for city gas mileage of 00 mpg, and such a prediction would be invalid, since 00 is outside the range of the data. The value of the intercept represents the predicted highway mileage for slope 0.0. The value of the intercept is an average value calculated from a sample. (c) Find the predicted highway mileage, ?̂ ,y^, for a car that gets 1515 miles per gallon in the city. (Enter your answer rounded to three decimal places.) ?̂ =y^= mpg Find the predicted highway mileage, ?̂ ,y^, for a car that gets 2323 miles per gallon in the city. (Enter your answer rounded to three decimal places.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 12091209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line

highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city mpg)

for predicting highway mileage from city mileage.

(a) What is the slope of this line? (Enter your answer rounded to three decimal places.)

What does the numerical value of the slope tell you?

On average, highway mileage decreases by 0.9930.993 mpg for each additional mpg in city mileage.

On average, highway mileage increases by 0.9930.993 mpg for each additional mpg in city mileage.

For every 7.9037.903 mpg in city gas mileage, highway gas mileage increases about 0.9930.993 mpg.

Highway gas mileage increases with city gas mileage by 7.9037.903 mpg for each additional mpg in city mileage.

On average, highway mileage increases by 7.9037.903 mpg for each additional mpg in city mileage.

(b) What is the intercept? (Enter your answer rounded to three decimal places.)

intercept:

mpg

Why is the value of the intercept not statistically meaningful?

The value of the intercept represents the predicted highway mileage for city gas mileage of 00 mpg, and such a car does not exist.

The value of the intercept represents the predicted highway mileage for city gas mileage of 00 mpg, and such a prediction would be invalid, since 00 is outside the range of the data.

The value of the intercept represents the predicted highway mileage for slope 0.0.

The value of the intercept is an average value calculated from a sample.

(c) Find the predicted highway mileage, ?̂ ,y^, for a car that gets 1515 miles per gallon in the city. (Enter your answer rounded to three decimal places.)

?̂ =y^=

mpg

Find the predicted highway mileage, ?̂ ,y^, for a car that gets 2323 miles per gallon in the city. (Enter your answer rounded to three decimal places.)

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