Nielsen Media Research produces two measures of actual TV viewership. One is the

Question

Nielsen Media Research produces two measures of actual TV viewership. One is the % of households that is watching a program relative to all households that have a TV set. The other indicator is for market share: the % of households that is watching the program relative to all households that are currently watching something on TV. The data presented below refer to the TV ratings according to these two measures for watching major league baseball over an interval of 9 years.

Viewership rating among households with TV set

Viewership share among households watching TV

a) Give a scatterplot for these two variables, with the first variable as your abscissa. b) « Eyeballing it », does it appear as though there is a relationship between them? Explain why or why not.
c) Calculate and interpret the sample covariance.

d) Calculate and interpret the sample correlation coefficient. What conclusion do you draw based on that value as far as the statistical relationship between the two variables is concerned?

Viewership rating among households with TV set

Viewership share among households watching TV

  19  17  17  14  16  12  15  12  13  

  32  28  29  24  26  20  24  20  22  

Explanation / Answer

Scatter plot

Eyeballing, there seems to a positive correlation between the two variables => viewership share among households watching TV increases when Viewrship rating among households with TV set increases

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b) Covariance = 8.889

c) Correlation = 0.99 => Near-exact positive correlation (highest possible = 1) means that there is a direct relationship between the two variables where increase in 1 variable leads to the increase in the other variable

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