John Howard, a Toronto real estate developer, has devised a regression model to help determine residential housing prices in southern Ontario. The model was developed using recent sales in a particular neighbourhood. The price ( Y ) of the house is based on the size (square footage 5 X ) of the house. The model is:
Y = 13 473 + 37.65X
The coefficient of correlation for the model is 0.63.
a) Use the model to predict the selling price of a house that is 1860 square feet.
b) An 1860-square-foot house recently sold for $95 000. Explain why this is not what the model predicted.
c) If you were going to use multiple regression to develop such a model, what other quantitative variables might you include?
d) What is the value of the coefficient of determination in this problem?