Question 7.39 - URBAN OWNERS 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 OWNERS

URBAN OWNERS

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

Since R2 is the square of the correlation, then the correlation, ‘r’ is as shown below:

correlation<- round(sqrt(0.28),2)
cat("The correlation is,", correlation)
## The correlation is, 0.53

We can tell if the correlation is positive or negative by looking at the pattern in which the dots are scattered in the scatter plot. There is an obvious downward trend in the scatter plot which denotes a a negative correlation between Urban population and homeownership.

(b) Examine the residual plot. What do you observe? Is a simple least squares fit appropriate for these data?

When i examined the residual plot, i observed that there is non constant variance. Look at how the dots fan out around the line. As \(x\) increases, so does variability.

Since the data does not meet the ’constant variablility requirement, i do not think that it is appropriate to use a simple least fit squares.