This data table contains the listed prices (in thousands of dollars) and the number of square feet for 28 homes listed by a realtor in the Seattle area.
(a) Create a scatterplot for the price of the home on the number of square feet. Does the trend in the average price seem linear?
(b) Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) If a homeowner adds an extra room with 500 square feet to her home, can we use this model to estimate the increase in the value of the home?
(e) A home with 2,690 square feet lists for $625,000. What is the residual for this case? Is it a good deal?
(f) Do the residuals from this regression show pat-terns? Does it make sense to interpret se as the standard deviation of the errors of the ft? Use the plot of the residuals on the predictor to help decide.