# Scatter diagram, covariance, correlation, weighted average

45. Nielsen Media 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 of 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 (Associated Press, Otober 27,2003)

Rating 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. Computer the sample correlation coefficient. What does this value tell us about the relationship between rating and share?

51. The daily high and low temperatures for 12 U.S cities are as follows (Weather Chanel, January 25,2004)

City High Low

Albany 9 -8

Boise 32 26

Cleveland 21 19

Denver 37 10

Des Moines 24 16

Detroit 20 17

Los Angeles 62 47

New Orleans 71 55

Portland 43 36

Providence 18 8

Raleigh 28 24

Tulsa 55 38

a. What is the sample mean daily high temperature?

b. What is the sample mean daily low temperature?

c. What is the correlation between the high and low temperatures?

53. Consider the following data and corresponding weights

Xi Weight(Wi)

3.2 6

2.0 3

2.5 2

5.0 8

a. Compute the weighted mean

b. Compute the samle mean of the four data values without weighting. Note the difference in the results provides by the two distribution.

55. Blooberg Personal Finance (July/August 2001) included the following companies in its recommended investment portfolio. For a portfolio value of $25,0000, the recommended dollar amounts allocated to each stock are shown.

Company Portfolio($) Estimate Growth Rate(%) Dividend Yield(%)

Citigroup 3000 15 1.21

General Electric 5500 14 1.48

Kimberly-Clark 4200 12 4.72

Oracle 3000 25 0.00

Pharmacia 3000 20 0.96

SBC Communications 3800 12 2.48

WorldCom 2500 35 0.00

a. Using the portfolio dollar amounts as the wights, what is the wighted average estimated growth rate for the portfolio?

b. What is the weighted average dividend yield for the portfolio.

65. The following date show the media expenditures ($ millons) and shipments in millions of barrels (bbls.) for 10 major brands of beer.

Brand Media Expenditures ($M) Shipments in bbls. (M)

Budweiser 120.0 36.3

Bud Light 68.7 20.7

Miller Lite 100.1 15.9

Coors Light 76.6 13.2

Busch 8.7 8.1

Natural Light 0.1 7.1

Miller Genuine Draft 21.5 5.6

Miller High Lite 1.4 4.4

Busch Light 5.3 4.3

Milwaukee's Best 1.7 4.3

a. What is the sample coraviance? Does it indicate a positive or negative relationship between media expenditures and shipments?

b. What is the sample correlation coefficient?

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The solution answers questions on scatter diagram, covariance, correlation, weighted average etc