Math Problem Statement

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 (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y=41.57-0.49x. This line is shown in the scatter plot below. (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?

Solution

According to the least-squares regression equation:

y=41.57−0.49xy = 41.57 - 0.49x

Where:

  • yy represents the selling price (in thousands of dollars).
  • xx represents the mileage (in thousands of miles).

The equation shows that for each unit increase in xx (which represents 1,000 miles), the selling price yy decreases by the slope value of the equation, which is −0.49-0.49.

Thus, for every additional 1,000 miles on the odometer, the price decreases by 0.49 thousand dollars, or $490.

Would you like further details or have any questions? Here are 5 related questions:

  1. How is the least-squares regression line calculated from a set of data points?
  2. What does the intercept (41.57) in this regression equation represent?
  3. How would the price change if the mileage increased by 10,000 miles?
  4. Can the regression equation predict prices for Cadets with very high or low mileage accurately?
  5. How does the correlation coefficient relate to the strength of this regression line?

Tip: In regression analysis, the slope tells you how much the dependent variable changes for a one-unit change in the independent variable.

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Bivariate Data Analysis

Formulas

y = 41.57 - 0.49x
Slope of the regression line = -0.49

Theorems

Least-Squares Regression Theorem

Suitable Grade Level

Grades 10-12

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