Question

The table below lists maintenance cost vs. the age of cars for a sample of seven cars. The goal was determine if there was a correlation between the age of a car and the cost to maintain it. The least squares regression equation describing the maintenance costs (Y′) vs. the age of the car (X) was determined to be

Y' = −4.75 + 2.8929X

Age of Car (yrs)	Maintenance Costs ($hundreds)
2	3
3	5
4	6
5	7
6	10
7	15
8	22

What is the standard error of estimate?

Multiple Choice

• 6.621

• 2.573

• 5.754

• 3.864

Answer 1

For this problem, we will first use the formula for correlation and then we will use R for getting the OLS estimator, the standard error for estimates and standard error for Residual.

For correlation measure we have used R to get the correlation. Here in this case the correlation measure has been 0.9360566 which is " Very High Positive Correlation ".

Coming back to the main analysis, we have analyzed the data in R and we got the following info -

The standard error for the Residual is 2.573 with 5 degrees of freedom

The standard error for the age of the vehicle variable is 0.4863 with p-value 0.00192 which is SIGNIFICANT at 95% confidence level.

I am uploading the image of the outcome which has come directly from R. Its for your reference.

The regression Result :

And the relation between x ( The age of the vehicle) and Y ( The maintenance cost) is given below in graph :

Hope this answer has helped you.

Thanks !!