Question

Elitis Ltd. plans to purchase a fuel-efficient new truck to use in its delivery services in a small region. The company considers several possible vehicles with the following parameters:



Truck Purchase cost in AU$ x Truck age inyears y

Truck model 1 17,500 3

Truck model 2 11,250 2

Truck model 3 2,850 9

Truck model 4 9,800 5

Truck model 5 8,900 8

Truck model 6 16,500 3

Truck model 7 21,300 2

Truck model 8 6,950 5

Truck model 9 15,400 3

Truck model 10 5,500 8

Based on the table above, complete the following tasks:

a Calculate the correlation coefficient.

b Calculate the linear regression model parameters.


c Estimate the cost of a 6-year-old truck.

Answer 1

Solution:

We are given the following data:

Cost (AU$)	Age (Year)
17500	3
11250	2
2850	9
9800	5
8900	8
16500	3
21300	2
6950	5
15400	3
5500	8

The correlation coefficient between given two variables is given as below:

	Cost (AU$)	Age (Year)
Cost (AU$)	1
Age (Year)	-0.840481572	1

Regression model for the prediction of dependent variable cost (AU$) based on independent variable age in years is given as below:

Regression Statistics
Multiple R	0.840481572
R Square	0.706409272
Adjusted R Square	0.669710431
Standard Error	3391.358996
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	221386723.3	221386723.3	19.24881695	0.00232579
Residual	8	92010526.73	11501315.84
Total	9	313397250
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	20550.4717	2305.785333	8.912569355	1.99089E-05	15233.32119	25867.62221
Age (Year)	-1865.72327	425.2508664	-4.38734737	0.00232579	-2846.353526	-885.0930148

The regression equation for the prediction of dependent variable cost based on independent variable age in years is given as below:

Cost (AU$) = 20550.4717 - 1865.72327*Age

Part a

The correlation coefficient between the dependent variable cost of the truck and independent variable age of truck is given as -0.840481572, which means there is a strong negative linear relationship or association exists between given two variables.

Part b

The regression equation for the prediction of the dependent variable cost of truck based on the independent variable age of truck is given as below:

Cost (AU$) = 20550.4717 - 1865.72327*Age

Where intercept for this regression equation = 20550.4717

Slope of regression equation = -1865.72327

Cost of a truck is decreased by $1865.72 as per increase in age by one year.

Part c

We are given age = 6 years

Regression equation is given as below:

Cost (AU$) = 20550.4717 - 1865.72327*Age

Cost (AU$) = 20550.4717 - 1865.72327*6

Cost (AU$) = 9356.13208

Estimated cost = AU$9356.13