Question

Question 9:

A car dealer wants to find the relationships of car prices related to 3 variables: “Year”, “Mileage” and “Horsepower”. Here is the Excel Output results with 30 observations:

	Coefficient	Standard Error	t-stat	p-value
Intercept	2501198.34	931631	2.684	0.012
Year	-1205.23	462.62	-2.60	0.014
Mileage	-0.850	0.23	-3.62	0.001
Horsepower	56.67	30.63	1.95	0.04

What is the 99% confidence interval for the slope of Horsepower?

(a) (56.67-2.756*30.63, 56.67+2.756*30.63)

(b) (56.67-2.771*30.63, 56.67+2.771*30.63)

(c) (56.67-2.763*30.63, 56.67+2.763*30.63)

(d) (56.67-2.779*30.63, 56.67+2.779*30.63)

Answer 1

Solution: Here we have given the Excel output for 30 observations.

We have to find the 99% confidence interval for the slope of Horsepower.

Confidence interval for slope= (Coefficient Critical value*Standard error)

Coefficient = 56.67, Standard error =30.63, n=30, =0.99

Degrees of freedom = n-2 = 30- 2 =28 ( In regression analysis t test n-2 degrees of freedom use)

Critical value for 28 degrees of freedom and 0.01 region =2.763----------(from t table)

So the option is c

(c) (56.67-2.763*30.63, 56.67+2.763*30.63)