A builder is interested in which types of homes earn a higher price. For a given number of square feet, the builder gathered prices of homes that use the space differently. In addition to price, the homes vary in the number of rooms devoted to personal use (such as bathrooms or bedrooms) and rooms devoted to social use (enclosed decks or game rooms). Because the homes are of roughly equal size (equal numbers of square feet), the more space devoted to private use, the less devoted to social use. The variable Private denotes the number of square feet used for private space and Social the number of square feet for social rooms.
(a) Would you expect to find collinearity in a multiple regression of Price on Private and Social? Explain.
(b) Rather than use both Private and Social as two variables in a multiple regression for Price, suggest an alternative that might in the end be simpler to interpret as well.