A consumer research company collected data for 16 models of sport utility vehicl

Question

A consumer research company collected data for 16 models of sport utility vehicles of various sizes. The research team measured the overall fuel economy and the distance between their front and rear axles (wheelbase) of each vehicle. The scatter plot and line of best fit is shown in the diagram below.

1. Which one of the following statements concerning the regression line is true?

            a.     There is a positive linear relationship between the two variables.

           b.     The slope is greater that 1.

            c.     The intercept is at or near 30.

            d.     Vehicles with larger wheelbases have the worst fuel economy.

.2. The slope of the regression line, b1, is at or near which of the following values?

            a.     –0.3

            b.     0

            c.     0.3

            d.     3

3.     The intercept of the regression line, b0, is at or near which of the following values?

            a.     20

            b.     30

            c.     60

            d.     160

4.      Juanita Douglas just bought a new red SUV that has a wheelbase of 115 inches. What overall fuel economy can she expect to obtain?

            a.     28 mpg

            b.     25 mpg

            c.     20 mpg

                     d.    15 mpg

5.              A –0.947 correlation coefficient has been found between two variables after examining 43 pairs of observations. What can be concluded?

            a.     There is a strong positive relationship between the two variables.

            b.     There is a strong negative relationship between the two variables.

            c.     There is a weak positive relationship between the two variables.

E 20 5 15 10 Wheelbase and Fuel Economy of SUVs 100 110 120 130 140 Wheelbase (inches)

Explanation / Answer

1:

Line is down to the right so it shows a negative relationship between the variables.

d.     Vehicles with larger wheelbases have the worst fuel economy.

2;

Slope must be negative. So option a is correct.

a.     –0.3

3:

Intercept shows the value of Y when x=0 so intercept must be near 60.

Option b is correct.

4:

The requried expected value is

y' = 60-0.3x = 30-0.3 * 115 = 25.5 mpg

So required estimate value should be near 25 mpg.

5:

b.     There is a strong negative relationship between the two variables.

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