Question

Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price and x = house size (sq ft) for houses in a large city. The true regression line is y = 22,500 + 46x and σ = 5000.

(a) What is the average change in price associated with one extra sq ft of space?

With an additional 100 sq ft of space?

(b) What proportion of 2000 sq ft homes would be priced over $120,000? (Round your answer to four decimal places.)

Under $110,000? (Round your answer to four decimal places.)

Answer 1

a)

average change in price associated with one extra sq ft of space =46

e average change in price associated with an additional 100 sq ft of space =46*100 =4600

b)

here for x=2000 sq ft; expected price =22500+46*2000=114500

hence proportion of 2000 sq ft homes would be priced over $120,000 =P(X>120000)=P(Z>(120000-114500)/5000)

=P(Z.>1.1) =0.1357

proportion of 2000 sq ft homes would be priced Under $110,000 =P(X<110000)=P(Z<-0.9)=0.1840