Linear Regression

43. The National Association of Home Builders ranks the most and least affordable housing markets, based on the proportion of homes that a family earning the median  income in that market could afford to buy. Data showing the median income ($1000s) and the median sale price ($1000s)  for a sample of 12 housing markets that appeared on the list of most affordable markets follow ( The Wall Street Journal  Almanac 1998).

Market Income (1,000?s) Price ($1000)

Syracruse 41.8 76

Springfield 47.7 91
Lima 40 65
Dayton 44.3 88
Beaumont 37.3 70
Lakeland 35.9 73
Baton Rouge 39.3 85
Nashua 56.9 118
Racine 46.7 81
Des Moines 48.3 89
St Paul 54.6 110
Wilmingtone 55.5 110

a. Use these data to develop an estimated regression equation that could be used to predict the median price for a market given the median income for the market. b. Did the estimated regression equation provide a good fit? Explain.

c. Develop a 95% confidence interval estimate of the median price for all homes sold in a market in which the median income is $40,100.

d. The median income in Binghamton, New York, was reported to be $40,100. Develop a 95% prediction interval estimate of the median sales price for homes sold in the Binghamton market.