Question

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)1 9 8.1 7 8 7.62 7 6.0 8 11 8.03 11 3.6 9 10 8.04 12 4.0 10 12 6.05 8 5.0 11 6 8.66 7 10.0 12 6 8.0(a) Determine the regression equation. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)a = ________b =_________

Answer 1

Answer:

a= 13.15 years

b= -0.62 years/$

Step-by-step explanation:

Hello!

Given the variables

Y: Age of a used car. (years)

X: Price of a sold used car. ($000)

The linear regression model is:

E(Y)= α + βXi

The estimated equation is:

^Y= a + bXi

$a= (\frac{sumY_i}{n} ) - b(\frac{sumX_i}{n} )$

a= 13.15 years

$b= \frac{(sumX_iY_i-\frac{(sumX_i)(sumY_i)}{n} }{sumX_i^2-(\frac{(sumX_i)^2}{n} )}$

b= -0.62 years/$

Then ^Y= 13.15 - 0.62Xi

Mean Y= 8.92

Mean X= 6.91

∑Y= 107

∑Y²=1009

∑X=82.90

∑X²=615.29

∑XY=712.9

Hope it helps!