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# 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.

- (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?
- (b) Construct a scatterplot of selling price vs. site area, and overlay this plot with the least squares line you found in part (a).
- (c) What proportion of variation in the selling price can be attributed to its linear relationship with site area?
- (d) Provide a 95% confidence interval for the mean selling price of a house with 8,000 square feet.
- (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.
- (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?
- (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?
- (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