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Correlation Analysis

45. Five observations taken for two variables follow

X 4 6 11 3 16
i

Y 50 50 40 60 30
i

a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.

47. Nielsen Median Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage oh households watching a program among those with televisions in use. The following data show the Nielsen television ratings and share data for the Major League Baseball World Series over a nine-year period.

Ratings 19 17 17 14 16 12 15 12 13
Share 32 28 29 24 26 20 24 20 22

A. Develop a scatter diagram with rating on the horizontal axis.
B. What is the relationship between rating and share? Explain
C. Compute and interpret the sample covariance.
D. Compute the sample correlation coefficient. What does this value tell us about the relationship between rating and share?

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The solution gives complete steps for analyzing the relationship between two variables using scatter diagram and correlation coefficient.

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