Question

a consumer magazine collected the following data for the fuel efficiency of cars (miles per gallon) compared to weight (thousands of pounds). homework help e = 49 - 8.4w w is the weight (1000s of pounds) and e is the fuel efficiency (mpg). a. describe the association between fuel efficiency and weight. b. cheetah motors has come out with a super lightweight sports utility vehicle (suv) that weighs only 2800 pounds. what does the model predict the fuel efficiency will be?

Explanation:

Part a

To describe the association, we analyze the linear equation \( e = 49 - 8.4w \). The slope of the line is -8.4, which is negative. In the context of the scatter plot (with a negative trend line), as the weight \( w \) (in thousands of pounds) increases, the fuel efficiency \( e \) (in mpg) decreases. The relationship appears linear (from the equation and the scatter plot's trend line) with a negative association, and the points seem to cluster around the line, indicating a moderately strong linear relationship.

Step 1: Convert weight to the correct unit

The weight of the SUV is 2800 pounds. Since \( w \) is in thousands of pounds, we divide 2800 by 1000. So \( w=\frac{2800}{1000} = 2.8 \).

Step 2: Substitute \( w = 2.8 \) into the equation

We use the equation \( e=49 - 8.4w \). Substitute \( w = 2.8 \) into the equation: \( e=49-8.4\times2.8 \).
First, calculate \( 8.4\times2.8 \): \( 8.4\times2.8=(8 + 0.4)\times2.8=8\times2.8+0.4\times2.8 = 22.4+1.12 = 23.52 \).
Then, calculate \( e = 49-23.52=25.48 \).

Answer:

There is a negative linear association between fuel efficiency and weight. As the weight of the car (in thousands of pounds) increases, the fuel efficiency (in mpg) decreases, and the relationship appears to be moderately strong and linear (supported by the linear model \( e = 49 - 8.4w \) and the scatter - plot trend).

Part b