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 = 22,500 + 47x and ? = 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.)

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A number of investigations have focused on the problem of assessing loads that can be manually handled in a safe manner. A particular article proposed using a regression model to relate the following dependent variable (y) to k = 3 independent (predictor) variables.

y = individual's rating of acceptable load (kg)
x1 = extent of left lateral bending (cm)
x2 = dynamic hand grip endurance (sec)
x3 = trunk extension ratio (N/kg)

Suppose that the model equation is the following and that ? = 4.

(a) What is the mean value of rating of acceptable load when extent of left lateral bending is 45 cm, dynamic hand grip endurance is 190 sec, and trunk extension ratio is 12 N/kg?


(b) If repeated observations on rating are made on different individuals, all of whom have the values of x1, x2, and x3 specified in Part (a), in the long run approximately what proportion of ratings will be between 23.7 kg and 39.7 kg? (Use Table 2 in Appendix A. Round your answer to four decimal places.)

Explanation / Answer

Q1 y = 22,500 + 47*x
sd = 5000

part A)

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

x =1

y = 22500 + 47*1 = 22547

x =100

y = 22500 + 47*100 =2254700

part B) x =2000

y = 22500 + 47*2000 =  116500

z =(116500-120000)/5000 =-0.7

pnorm(z,lower.tail = FALSE) = 0.7580363=0.7580

Q2 y = 30+0.90*x1+0.08*x2-4.50*x3+e

x1 =45
x2=190
x3 =12
y = 30+0.90*x1+0.08*x2-4.50*x3

=31.7

b) p(23.7<y<39.7)=p((23.7-E(Y))/S.D(Y) <Z<(39.7-E(y))/S.D(y) )=0.95

where z = (y-E(y))/S.D(y)

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