A. Suppose that y is the average price (in thousands of dollars) of a typical three-bedroom home in a large Canadian city. Fourteen consecutive observations y1, y2, . . . , 6-month intervals over 7 years. Att beginning of the eighth interval the government implemented steps to slow down the rate of the price increases. A ossible model for these data specifies that rices increase linearly with time until the he 8, at which time the rate of time point increase (slope) changes. Such a model consists of a pair of straight lines intersecting at time point 8. Formulate this as a linear model y = Xß + e. Explicitly define the parameters you are using and write out the X matrix. b. An alternative model specifies that the government's actions had no effect on prices, and that prices continued to increase at the same constant rate. Set up the appropriate linear model y = Xß + e.
c. Suppose you found that the residual sum of squares in (a) is 6.12 and that in (b) is 37.25. What evidence does this provide with regard to whether model (a) is better than model (b)?