The data shown in the following table were obtained from the 1990 Census. Included is information on

Question:

The data shown in the following table were obtained from the 1990 Census. Included is information on 26 randomly selected Metropolitan Statistical Areas (MSAs). Of interest are factors that potentially are associated with the rate of owner occupancy of housing units. Two variables are included in the data set: OWNEROCC = percentage of housing units that are owner-occupied (as opposed to renter-occupied); and OWN-COST = median selected monthly ownership costs (in $).
a. Based on the accompanying scatter diagram of OWNEROCC versus OWN-COST, does there appear to be a linear relationship between these two variables?

b. State the model for the straight-line regression of OWNEROCC (Y) on OWN-COST (X). Determine the least-squares estimates for this regression line. Interpret the estimated values of the slope and the intercept in the context of the problem.
c. Sketch the estimated line on the scatter diagram and assess the fit.
d. Test for the significance of the slope parameter of the model in part (b). Interpret your result.
e. Determine a 95% confidence interval for the true slope in part (d). Interpret your result with regard to the test mentioned in part (d).