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 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. With the aim of predicting the used selling price from the number of miles driven, we might examine the least-squares regression line, =y−41.990.51x . This line is shown in the scatter plot below. Based on the sample data and the regression line, complete the following. (a)For these data, mileages that are less than the mean of the mileages tend to be paired with used selling prices that are ▼(Choose one) the mean of the used selling prices. (b)According to the regression equation, for an increase of one thousand miles in Cadet mileage, there is a corresponding ▼(Choose one) of 0.51 thousand dollars in the used selling price. (c)From the regression equation, what is the predicted used selling price (in thousands of dollars) when the mileage is 20.9 thousand miles? (Round your answer to at least one decimal place.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 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. With the aim of predicting the used selling price from the number of miles driven, we might examine the least-squares regression line, =y−41.990.51x

. This line is shown in the scatter plot below.

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

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

(b)According to the regression equation, for an increase of one thousand miles in Cadet mileage, there is a corresponding ▼(Choose one) of

0.51

thousand dollars in the used selling price.

(c)From the regression equation, what is the predicted used selling price (in thousands of dollars) when the mileage is

20.9

thousand miles? (Round your answer to at least one decimal place.)

(d)What was the observed used selling price (in thousands of dollars) when the mileage was

20.9

thousand miles?

line is shown in the scatter plot below.
Used selling
price, y
(in thousands) (in thousands
of dollars)
Mileage, x
25.5
26.6
29.6
27.8
40-
24.1
28.0
15.6
35.0
22.9
32.9
26.6
30.5
**
34.4
26.1
20.9
30.4
38.8
21.7
37.8
22.6
22.6
31.1
24.5
30.1
23.5
27.9
Mileage, x
27.6
30.3
(in thousands)
20.8
31.4
27.9
25.6
Used selling price, y
(in thous ands of dollars)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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