Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price (in dollars) and x = house size (in square feet) for houses in a large city. The population regression line is y = 23,000 + 47x and σ = 5000.
a. What is the average change in price associated with one extra square foot of space? With an additional 100 sq. ft. of space?
b. What proportion of 1800 sq. ft. homes would be priced over $110,000? Under $100,000?