You are strongly encouraged to use technology: Put data as L1 for x and L2 for y. Then go to STAT -

TESTS -

Select LinRegTTest and fill out the required fields. Choose

0

(Means null hypothesis is

no significant linear correlation, so you can use your P-value to check the significance of r, assume

0.05

)]

1.

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the

weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg)

X

29

46

29

47

23

40

34

52

Y

31

20

23

13

29

17

21

14

a.

Compute the value of the sample correlation coefficient r. (Round your value for r to be

three decimal places)

b.

Find the equation of the least-squares line

y a bx

(Round your value for a and b to be

three decimal places)

c.

Find the value of the coefficient of determination

2

.

r

What percentage of the variation in y

can be explained by the corresponding variation in x and the least - squares line? What

percentage is unexplained? (Round your value for r to be three decimal places)

d.

Suppose a car weighs x = 45 (hundreds of pounds), what does the least - squares line

forecasts for y = miles per gallon? (Round your answer to two decimal places.