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# Correlation and regression analysis

See attachment for the problems I am struggling with.

Thanks in advance for any help provided.

In the following exercises, construct a scatter plot, find the value of the linear correlation coefficient r, find the critical value of r from Table A-6 by using &#945; = 0.05 and determine if there is a linear correlation between the two variables.

Table A-6
Critical Values of the Pearson Correlation Coefficient r
n &#945; = .05 &#945; = .01
4 .950 .999
5 .878 .959
6 .811 .917
7 .754 .875
8 .707 .834
9 .666 .798
10 .632 .765
11 .602 .735
12 .576 .708
13 .553 .684
14 .532 .661
15 .514 .641
16 .497 .623
17 .482 .606
18 .468 .590
19 .456 .575
20 .444 .561
25 .396 .505
30 .361 .463
35 .335 .430
40 .312 .402
45 .294 .378
50 .279 .361
60 .254 .330
70 .236 .305
80 .220 .286
90 .207 .269
100 .196 .256

#17 Listed below are the chest sizes (in inches) and weights (in pounds) of randomly selected bears that were anesthetized and measured. Because it is much more difficult to weigh a bear than to measure its chest size, the presence of a correlation could lead to a method for estimating weight based on chest size. Is there a linear correlation between chest size and weight?

Chest size
26
45
54
49
35
41
41
49
38
31
Weight 80 344 416 348 166 220 262 360 204 144

#21 The New York Post published the annual salaries (in millions) and the number of viewers (in millions), with results given below for Oprah Winfrey, David Letterman, Jay Leno, Kelsey Grammer, Barbara Walters, Dan Rather, James Gandolfini, and Susan Lucci, respectively. Is there a correlation between salary and number of viewers? Which of the listed stars has the lowest cost per view? Highest cost per viewer?

Salary 100 14 14 35.2 12 7 5 1
Viewers 7 4.4 5.9 1.6 10.4 9.6 8.9 4.2

#23 In "The Effects of Temperature on Marathon Runner's Performance" by David Martin and John Buoncristiani high temperatures and times (in minutes) were given for women who won the New York City marathon in recent years. Results are listed below. Is there a correlation between temperature and winning time? Does it appear that winning times are affected by temperature?

x (temperature) 55 61 49 62 70 73 51 57
y (time) 145.283 148.717 148.300 148.100 147.617 146.400 144.667 147.533

In the following exercises use the same data sets as the previous exercises. In each case, find the regression equation, letting the first variable be the independent (x) variable. Find the indicated predicted values.

#17 Find the best predicted weight (in pounds) of a bear with a chest size of 50 inches.

Chest size
26
45
54
49
35
41
41
49
38
31
Weight 80 344 416 348 166 220 262 360 204 144

#21 Find the best predicted number of viewers for a television star with a salary of \$2 million.

Salary 100 14 14 35.2 12 7 5 1
Viewers 7 4.4 5.9 1.6 10.4 9.6 8.9 4.2

#23 Find the best predicted winning time for the 1990 marathon when the temperature was 73 degrees. How does that predicted winning time compare to the actual winning time of 150.750?

x (temperature) 55 61 49 62 70 73 51 57
y (time) 145.283 148.717 148.300 148.100 147.617 146.400 144.667 147.533