Question

At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you. X = {5, 10, 12, 14, 15} Y = {500, 400, 300, 200, 100}

1) What is the value for S^2?

2) What is the value for s?

3) Construct a 95% confidence interval for B1. what is the upper bound and lower bound?

4) does the data provide sufficient evidence to indicate that X contributes to the prediction of Y?

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	5	500	25	250000	2500
	10	400	100	160000	4000
	12	300	144	90000	3600
	14	200	196	40000	2800
	15	100	225	10000	1500
Total	56	1500	690	550000	14400

1)

The   value for S^2 is

2)

S =SE  = 52.5363

3)

The required confidence interval is (-59.31, -17.12).

4)

Since confidence interval does not contain zero so we can conclude that the data provides sufficient evidence to indicate that X contributes to the prediction of Y.