heleast-squares regression equation is

y=649.4x+16,623 where y is the median income and x is the percentage of 25 years and older with at least abachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.6998. Complete parts(a) through(d).

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Bachelor's%

MedianIncome

a) Determine which variable is the likely explanatory variable and which is the likely response variable.

The explanatory variable is the miles per gallon and the response variable is the weight.

The explanatory variable is the weight and the response variable is the miles per gallon.

Your answer is correct.

(b) Draw a scatter diagram of the data. Choose the correct scatter plot.

A.

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30

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mpg

Weight(lbs)

A scatter diagram has a horizontal axis labeled "miles per gallon" from 15 to 30 in increments of 5 and a vertical axis labeled "Weight (pounds)" from 2500 to 4000 in increments of 500. The following 5 approximate points are plotted, listed here from left to right: (18, 2650); (19, 3300); (20, 2600); (26, 4000); (27, 3500). The points have no apparent pattern from left right.

B.

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4000

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Weight(lbs)

mpg

A scatter diagram has a horizontal axis labeled "Weight (pounds)" from 2500 to 4000 in increments of 500 and a vertical axis labeled "miles per gallon" from 15 to 30 in increments of 5. The following 5 approximate points are plotted, listed here from left to right: (2600, 27); (2650, 26); (3300, 19); (3500, 20); (4000, 18). The points follow the general pattern of a straight line that falls from left to right.

Your answer is correct.

C.

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30

2500

4000

mpg

Weight(lbs)

A scatter diagram has a horizontal axis labeled "miles per gallon" from 15 to 30 in increments of 5 and a vertical axis labeled "Weight (pounds)" from 2500 to 4000 in increments of 500. The following 5 approximate points are plotted, listed here from left to right: (18, 4000); (19, 3300); (20, 3500); (26, 2650); (27, 2600). The points follow the general pattern of a straight line that falls from left to right.

D.

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4000

15

30

Weight(lbs)

mpg

A scatter diagram has a horizontal axis labeled "Weight (pounds)" from 2500 to 4000 in increments of 500 and a vertical axis labeled "miles per gallon" from 15 to 30 in increments of 5. The following 5 approximate points are plotted, listed here from left to right: (2600, 20); (2650, 18); (3300, 19); (3500, 27); (4000, 26). The points have no apparent pattern from left right.

(c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon.

r

negative 0.944

0.944

(Round to three decimal places asneeded.)

(d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon based on the scatter diagram and the linear correlation coefficient.

Because the correlation coefficient is negative

and the absolute value of the correlationcoefficient,

negative 0.944

0.944, is greater

than the critical value for this dataset,

0.878

0.878, a negative

linear relation exists between the weight of a car and its miles per gallon.

(Round to three decimal places asneeded.)