The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.63 - 0.46x . This line is shown in the scatter plot below. Mileage, x (in thousands) Used selling price, y (in thousands of dollars) 23.9 29.5 37.6 22.6 20.8 30.9 23.3 33.1 28.3 26.1 27.3 29.9 27.7 29.8 20.9 30.3 25.8 27.2 34.4 25.9 23.9 27.4 23.8 27.5 23.2 31.4 15.6 34.0 29.4 27.7 Send data to calculator Used selling price (in thousands of dollars) y 20 25 30 35 40 x 15 20 25 30 35 40 Mileagex (in thousands) Based on the sample data and the regression line, complete the following. (a) For these data, used selling prices that are less than the mean of the used selling prices tend to be paired with mileages that are ▼(Choose one) the mean of the mileages. (b) According to the regression equation, for an increase of one thousand miles in Cadet mileage, there is a corresponding decrease of how many thousand dollars in the used selling price?

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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Question

The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.63 - 0.46x

. This line is shown in the scatter plot below.

Mileage, x (in thousands)	Used selling price, y (in thousands of dollars)
23.9	29.5
37.6	22.6
20.8	30.9
23.3	33.1
28.3	26.1
27.3	29.9
27.7	29.8
20.9	30.3
25.8	27.2
34.4	25.9
23.9	27.4
23.8	27.5
23.2	31.4
15.6	34.0
29.4	27.7

Send data to calculator

Used selling price (in thousands of dollars)	y 20 25 30 35 40 x 15 20 25 30 35 40
	Mileagex (in thousands)

Based on the sample data and the regression line, complete the following.

(a)	For these data, used selling prices that are less than the mean of the used selling prices tend to be paired with mileages that are ▼(Choose one) the mean of the mileages.

(b)	According to the regression equation, for an increase of one thousand miles in Cadet mileage, there is a corresponding decrease of how many thousand dollars in the used selling price?