# Linear Correlation Assignments

In this assignment, you should solve four questions, where you will be asked to calculate a linear correlation coefficient and determine whether there is a linear correlation between the two given variables.

Solve the following:

1. Listed below are baseball team statistics consisting of the proportions of wins and the result of this difference: Difference (number of runs scored) - (number of runs allowed). The statistics are from a recent year, and the teams are NY?Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City.

Difference

163

55

-5

88

51

16

-214

Wins

0.599

0.537

0.531

0.481

0.494

0.506

0.383

a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using ? = 0.05.

b. Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference?

2. One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in °F:

Chirps in 1 min

882

1188

1104

864

1200

1032

960

900

Temperature (°F)

69.7

93.3

84.3

76.3

88.6

82.6

71.6

79.6

a. Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using ? = 0.05.

b. Is there a linear correlation between the number of chirps

https://brainmass.com/statistics/correlation/linear-correlation-assignments-482977

#### Solution Summary

Linear correlation assignments are examined.

Pearson Correlation Assignment

Please look over what I have done and help me with the rest. My answers are in brackets.

2. What information is provided by the numerical value of the Pearson correlation?

(The sample correlation coefficient, usually denoted r, is a numerical measure of the strength and the direction of the sample linear relationship between two variables. The value of r is always a number from -1to1. If r is positive, then the sample data indicate a positive linear relationship between the two variables; if r is negative, then the sample data indicate a negative linear relationship between the two variables. The closer that r is to the extreme values -1and1, the stronger the linear relationship indicated by the sample data. When r=0, the sample data indicate no linear relationship between the two variables).

6b. For the following scores,

X Y

1 3

3 5

2 1

2 3

b. Compute the Pearson correlation.

14.I identifying individuals with a high risk of Alzheimer's disease usually involve a long series of cognitive tests. However, researchers have developed a 7 minute screen which is a quick and easy way to accomplish the same goal. The question is whether the 7 minute screen is as effective as the complete series of tests. To address this question, Ijuin et al. (2008). Administered both tests to a group of patient and compared the results. The following data and compared the results. The following data represent results similar to those obtained in the study.

Weight (X) Income (Y)

4 156

3 88

5 49

2 73

1 45

3 92

1 53

5 148

Chapter 16

10. For the following scores,

(X) (Y)

3 6

6 1

3 4

3 3

5 1

Reference

Richard Johnson (2006), probability and Statistics for Engineers, 7th edition, Prentice Hall.

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