The homeownership rate in the U.S. was 67.4% in 2009. In order to determine if homeownership is linked with income, 2009 state level data on the homeownership rate (Ownership) and median household income (Income) were collected. A portion of the data is shown below; the complete data can be found on the text website, labeled Home Ownership.
a. Estimate: Ownership = β0 + β1 Income + ε.
b. At the 5% significance level, is Income linearly related to Ownership? Show the steps of a hypothesis test using the critical value approach.
c. Construct a 95% confidence interval for the expected value of Ownership if Income is $50,000.
d. Compare the above confidence interval with a 95% prediction interval for Ownership.