Question

Spring 2019 Exam 3 April 12, 8:00 PM Q5. The owner of Maumee Ford-Volvo wants to study the relation 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 (x) Price v) 1 9 28100 6000 3600 4000 5000 10000 7600 8000 4 12 9 10 8000 10 11 6 12 6 6000 8600 8000 Draw the scatter diagram. Determine the correlation coefficient. Find the regression equation. Consider the age of car as the independent variable (a), and a. b. c. the selling price as dependent variable (). You need to find a, b for the following equation d. What is the predicted selling price for a car of the age 10.5 years.

Answer 1

Scatter Plot 12000 10000 8000 6000 4000 2000 10 12 14

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$

r = -0.544

((12+71 2900)-107+82900 )/(V(12 * 1009) _ (107)2)(12 * 615290000)-(82900)2) r

Equation of regression line is $\hat{Y} = a + bX$
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = -478.756

b = (12 * 712900-107 * 82900)/(12 * 1009-(107)2)

$a =( \Sigma Y - ( b * \Sigma X) ) / n$
a =( 82900 - ( -478.7557 * 107 ) ) / 12
a = 11177.238
Equation of regression line becomes

Y- 11177.2382 -478.7557X

When X = 10.5
$\hat{Y}$= 11177.238 + -478.756 X
$\hat{Y}$ = 11177.238 + -478.756 * 10.5
$\hat{Y}$ = 6150.3