ata on pollution and cost of medical care for elderly people are shown here. The

Question

ata on pollution and cost of medical care for elderly people are shown here. The following data give a measure of pollution (micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographic regions of the United States:

(a) Compute the six residuals. (Round your answers to two decimal places.)

(b) What is the value of the correlation coefficient for this data set? (Round your answer to three decimal places.)
r =   

Does the value of r indicate that the linear relationship between pollution and medical cost is strong, moderate, or weak?

Moderately strong positive

Moderately strong negative

Strong positive

Strong negative

Weak

Region Pollution Cost of
Medical
Care North 31.9 927 Upper South 33.7 903 Deep South 34.0 980 West South 28.7 984 Big Sky 32.3 964 West 41.9 911

Explanation / Answer

yhat is given in Yi' and residual in Y-Yi'

b)( r=Sxy/(SSx *SSy)1/2=-0.58

c)Moderately strong negative

x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi') 31.9 927 3.42 318.03 16280.64 953.5118 26.512 33.7 903 0.00 1750.03 38115.74 945.0679 42.068 34 980 0.06 1236.69 -32030.97 943.6606 -36.339 28.7 984 25.50 1534.03 -35881.89 968.5233 -15.477 32.3 964 2.10 367.36 -17490.22 951.6354 -12.365 41.9 911 66.42 1144.69 30549.24 906.6011 -4.399 Total 202.50 5669.00 97.52 6350.83 -457.45 mean 33.75 944.83 SSx Ssy Sxy

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