a) To control for a home's type in a regression model, you would include dummy variables for each type of home. For example, you would create two dummy variables: one for townhomes and one for condos. The reference category would be single-family houses. This way, the regression model can account for the different effects of each type of home on sale prices.
b) The regression model that includes controls for home type, square footage, and number of bedrooms can be written as:
Sale Price = β0 + β1(Type of Home) + β2(Square Footage) + β3(Number of Bedrooms) + ε
In this model, β0 represents the intercept, β1 represents the coefficients for the dummy variables representing the type of home, β2 represents the coefficient for square footage, β3 represents the coefficient for the number of bedrooms, and ε represents the error term.
c) The interpretation of the estimated coefficients for each variable from part b would be as follows:
- β0 (Intercept): This represents the estimated average sale price for single-family houses (the reference category) when square footage and number of bedrooms are held constant.
- β1 (Type of Home): These coefficients represent the estimated average difference in sale price between townhomes and single-family houses, and between condos and single-family houses, when square footage and number of bedrooms are held constant.
- β2 (Square Footage): This coefficient represents the estimated change in sale price for a one-unit increase in square footage, when the type of home and number of bedrooms are held constant.
- β3 (Number of Bedrooms): This coefficient represents the estimated change in sale price for a one-unit increase in the number of bedrooms, when the type of home and square footage are held constant.
It is important to note that the interpretation of the coefficients assumes all other variables in the model are held constant.