Suppose that a simple linear regression model is appropriate for describing the

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 = 22,000 + 47x and sigma = 4000. (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 1800 sq ft homes would be priced over $110,000? (Round your answer to four decimal places.) Under $100,000? (Round your answer to four decimal places.)

Explanation / Answer

Answer:

a).

$47

b).

$4700

c).

when x=1800, y =22000+47*1800 =106600

z value for 110000, z=(110000-106600)/4000 =0.85

P( x >110000) = P( z >0.85) =0.1977

d).

z value for 100000, z=(100000-106600)/4000 = -1.65

P( x <100000) = P( z <-1.65) =0.0495

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