Question

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 = 22,500 + 46x and σ = 5,000.

(a)

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

$

What is the average change in price associated with an additional 100 sq. ft of space?

$

(b)

Approximately what proportion of 1,900 sq ft homes would be priced over $110,000? (Round your answer to four decimal places.)

Approximately what proportion of 1,900 sq ft homes would be priced under $100,000? (Round your answer to four decimal places.)

Answer 1

Answer:

Given,

y = 22500 + 46x

standard deviation = 5000

a)

The average change in price associated with one extra square feet of space is 46

The average change in price associated with 100 extra square feet of space is

y^ = 22500 + 46*100

= 22500 + 4600

= 27100

The average change in price associated with 100 extra square feet of space is 27100

b)

Here x = 1900

y = 22500 + 46*1900

= 109900

P(y > 110000) = P((y-u)/s > (110000 - 109900)/5000)

= P(z > 0.02)

= 0.4920217 [since from z table]

= 0.4920

= 49.2% of 1900 sq.ft homes would be priced over $110000

P(y < 100000) = P((y-u)/s < (100000 - 109900)/5000)

= P(z < -1.98)

= 0.0238518 [since from z table]

= 2.39% of 1900 sq.ft homes would be priced under $100000.