A realtor randomly samples homeowners who have purchased homes in the last 2 years and records their income, \(y\), and home purchase price, \(p\) (the population is large enough that one can consider this a random sample with replacement):

(a) Calculate the sample covariance between income and home price.

(b) Calculate the sample correlation between income and home price.

(c) Calculate the linear function of income of the form \(\hat{p}=a+b y\) that is minimum distance from the home price observations.

(d) Discuss the extent to which there is a linear relationship between income and home price.

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Income Price 21,256 49,412 97,530 170,249 Income 37,589 137,557 24,759 56,856 67,598 18,369 45,828 83,198 35,890 73,703 46,873 38,749 80,050 24,897 57,893 11,0658 36,954 Price 74,574 232,097 124,309 144,103 92,600 61,763 77,971