Use a calculator to verify that ?x = 24.3, ?x2 = 87.47, ?y = 54.2, ?y2 = 468.56 and ?xy = 194.66. Compute r. (Round to 3 decimal places.)

Use a calculator to verify that ?x = 1.951, ?x2 = 0.550, ?y = 30.4, ?y2 = 150.72 and ?xy = 8.806. Compute r. (Round your answer to three decimal places.)

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

x

3

2

11

16

26

36

y

44

54

71

100

150

200

Complete parts (a) through (e), given ?x = 94, ?y = 619, ?x2 = 2362, ?y2 = 82,393, ?xy = 13,721, and r ? 0.991.

(b) Verify the given sums ?x, ?y, ?x2, ?y2, ?xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

?x =

?y =

?x2 =

?y2 =

?xy =

r =

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x

=

y

=

=

+ x

Find the value of the coefficient of determination r2. 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 answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained

%

unexplained

%

(f) The calves you want to buy are 22 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)

Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.

x

37

47

57

67

77

87

y

5

8

10

17

32

43

Complete parts (a) through (e), given ?x = 372, ?y = 115, ?x2 = 24814, ?y2 = 3351, ?xy = 8475, and r ? 0.949.

(b) Verify the given sums ?x, ?y, ?x2, ?y2, ?xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

?x =

?y =

?x2 =

?y2 =

?xy =

r =

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x

=

y

=

=

+ x

Find the value of the coefficient of determination r2. 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 answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =

explained

%

unexplained

%

(f) Predict the percentage of all fatal accidents due to failing to yield the right of way for 75-year-olds. (Round your answer to two decimal places.) %

After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a 1% level of significance, test the claim that the amount contributed to the library fund is independent of ethnic group.