Question

Emily Smith decides to buy a fuel-efficient used car. Here are several vehicles she is considering, with the estimated cost to purchase and the age of the vehicle.

Vehicle	Estimated Cost	Age
Honda Insight	$6355	7
Toyota Prius	$18732	2
Toyota Prius	$9963	6
Toyota Echo	$6793	5
Honda Civic Hybrid	$16310	2
Chevrolet Prizm	$2475	8
Mazda Protege	$2808	10
Toyota Corolla	$7073	9
Acura Integra	$8978	8
Scion xB	$11213	2
Scion xA	$9463	3
Mazda3	$15055	2
Mini Cooper	$22850	3

1. Find the correlation coefficient

2. Find the coefficient of dedtermination

3. Develop a simple linear regression equation for these data.

4. Interpret the meaning of the slope

5. Estimate the cost of a five-year old car

Conduct the hypothesis test to determine whether the regression slope coefficient is equal to 0. Test using a significance level of 0.10.

1. State the null and alternate hypothesis

2. Compute the value of the test statistic.

3. Compute the p-value

4. What is your decision regarding the null hypothesis? Interpret the result.

**Please circle and label your answers. Thank you!!!**

Answer 1

Solutiona:

install analysis tool pak in excel..
Go to data >data analysis>correlation you will get the correlation a matrix as below

	Estimated Cost	Age
Estimated Cost	1
Age	-0.77852	1

From above matix,correlation coefficient=r=-0.77852

there exists a positive relationship between estimated cost and age of car

2. Find the coefficient of dtermination

rsq=r*r=-0.77852*-0.77852

=0.6060934

=0.6060934*100

=60.61%

Explained variance=60.61%

unexplained variance=100-explained variance=100-60.61=39.39%

3. Develop a simple linear regression equation for these data.

In excel after installing analyis tool pak .

Go to data >data analysis >regression

select y as estimated cost

x as age

you will get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.778518516
R Square	0.60609108
Adjusted R Square	0.570281179
Standard Error	3992.03696
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	269726657.1	2.7E+08	16.92524	0.001718
Residual	11	175299950	15936359
Total	12	445026607.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	18777.06286	2270.803927	8.268905	4.76E-06	13779.06	23775.07
Age	-1582.594286	384.6823069	-4.11403	0.001718	-2429.27	-735.914

from above output:

Estimated cost= 18777.06286-1582.594286*age

4. Interpret the meaning of the slope

slope =-1582.594286

as age increases by 1 year,predicted estimated cost of car decreases by $ 1582.594286.