Use the data set below to complete this exercise.
A real estate association in a suburban community would like to study the relationship between the size of a single-family house (as measured by the number of rooms) and the selling price of the house (in $thousands). Two different neighborhoods are included in the study, one on the east side of the community (coded 0) and the other on the west side (coded 1). A random sample of 20 houses was selected.
1. Calculate the regression equation using Number of Rooms and Neighborhood to predict Selling Price. (1 point)
2. If α = 0.01, what decision would you make about the overall model? (1 point)
3. If α = 0.01, determine whether each independent variable makes a contribution to the regression model. What would be your decision for each independent variable? (1 point)
4. Interpret the regression coefficients found in #1.
a. Holding constant the effect of neighborhood, if you add an additional room to a house, how will the mean selling price change? (1 point)
b. For a given number of rooms, a west neighborhood house is estimated to ______________ (increase/decrease/stay the same) the mean selling price over an east neighborhood house by _______________. (1 point)
5. Add an interaction term to the model. Show the coding for the new variable to be used in the analysis. (1 point)
6. Calculate the new regression equation for the data using all three independent variables. (1 point)
7. If α = 0.01, determine whether the interaction term makes a significant contribution to the model. (1 point)
8. On the basis of the results in #3 and #7, which model would you choose? Why? (2 points)