The file housing.txt contains data on 28 houses. (a) Suppose we want to use linear regression to predict a house’s selling price based on the total…

1. The file housing.txt contains data on 28 houses.

1. (a) Suppose we want to use linear regression to predict a house’s selling price based on the total area of the property (listed under site.area, in thousands of square feet). What least squares line do we obtain?
2. (b) Construct a scatterplot of selling price vs. site area, and overlay this plot with the least squares line you found in part (a).
3. (c) What proportion of variation in the selling price can be attributed to its linear relationship with site area?
4. (d) Provide a 95% confidence interval for the mean selling price of a house with 8,000 square feet.
5. (e) Suppose a new house of 8,000 square feet comes on the market. Compute a 95% prediction interval for the selling price of this house.
6. (f) Repeat parts (a), (b), and (c), but this time regress selling price against number of rooms (column rooms in the data). Does number of rooms appear to be a better predictor of selling price?
7. (g) Now consider a multiple regression model that uses site area and number of rooms to predict selling price. The relevant R command is lm(sellingprice ∼ site.area + rooms). What least squares line do we obtain, and what is the associated R2 value?
8. (h) Use part (g) to compute a point estimate of the mean selling price of a house with 7,000 square feet and 6 rooms. 

housing.txt

index 1 local bathrooms site.area living.area garages rooms bedrooms age material style fireplace sellingprice7 4 42 3 1 0 25.97 4 62 1 1 0 29.56 3 40 2 1 0 27.96 3 54 4 1 0 25.96 3 42 3 1 0 29.96 3 56 2 1 0 29.97 3 51 2 1 1 30.96 3 32 1 1 0 28.92.0 10 5 42 2 1 1 84.99 5 14 4 1 1 82.96 3 32 1 1 0 35.96 3 30 1 2 0 31.55 2 30 1 2 0 31.06 3 32 2 1 0 30.95 2 46 4 1 1 30.06 3 32 1 1 0 28.98 4 50 4 1 0 36.97 3 22 1 1 1 41.96 3 17 2 1 0 40.57 3 23 3 3 0 43.96 3 40 4 1 1 37.56 3 22 1 1 0 37.98 4 50 1 1 1 44.56 3 44 4 1 0 37.98 4 48 1 1 1 38.93 1 3 0 36.98 4 31 4 1 0 45.86 3 30 3 1 1 41.0