7.39 Urban homeowners, Part II. Exercise 7.33 gives a scatterplot displaying the relationship between the percent of families that own their home and the percent of the population living in urban areas. Below is a similar scatterplot, excluding District of Columbia, as well as the residuals plot. There were 51 cases.

Urban

Urban

  1. For these data, R2 = 0.28. What is the correlation? How can you tell if it is positive or negative?

The correlation = sqrt(R2) = sqrt(0.28) = 0.53. R2 = 0.28 means the percent of the population living in urban areas explains 28% of the variability of the percent of families that own their home. The other 78% is explained by something else or inherent randomness in the data. As shown in the scatterplot, there is negative association between these two variables. As the percent of urban population goes up, the percent of families who own their home goes down.

  1. Examine the residual plot. What do you observe? Is a simple least squares fit appropriate for these data? The residuals appear to be fan shaped indicating non-constant variance. Therefore, these data do not meet the conditions required for fitting a least squares line.