Question

The regional transit authority for a major metropolitan area wants to determine whether there is any linear relationship between the mileage of a bus and the market resale value of the bus. A very small random sample resulted in the following data:

Bus Mileage	Resale Value
(In 1000 of Miles)	(In $1000)
5	58
3	90
4	85
2	96
5	64
5	57

a. Use the method of OLS to compute the slope and intercept of the sample linear regression line. You need to decide which one is the defendant variable. In addition, write down the estimated sample regression line. Show all of your computations.

b. Explain the meaning of estimated sample intercept and slope in the context of this problem and in plain English.

c. Use a level of significance of 0.05 to check if the population slope is statistically equal to or different from zero. What is your conclusion? Why? Make sure the null and alternative hypotheses are explained in plain English. Also, show the decision rule and critical points or the p-value.

d. Compute the value of coefficient of determination. Explain what it means in the context of this problem and in plain English.

Answer 1

a) From the given data

S.No.	X	Y	X^2	Y^2	XY
1	5	58	25	3364	290
2	3	90	9	8100	270
3	4	85	16	7225	340
4	2	96	4	9216	192
5	5	64	25	4096	320
6	5	57	25	3249	285
Total:	24	450	104	35250	1697

b) Slope = -12.875 which is less than 0
therefore, there is negative correlation between Bus Mileage and Resale value of Bus

i.e. as Bus mileage every 1 unit(in 1000 of Miles) increase, the bus resale value is decreased by 12.875 (in $1000) and vice-versa

Intercept: 126.5
If Bus Milleage is zero then Resale value is 126.5 (in $1000)
which is meaning less since Zero is not contained in the given data (Bus mileage)

c) From MINITAB output,

Test Statistic of Bus Mileage : t = -12.88/2.33 = -5.52

P-value is 0.005

since P-value < alpha 0.05 so we reject H0

Thus w conclude that Bus Mileage is significant

d) R2 = SSR / SST = 1326.12 / 1500 =0.8841

R2 = 88.41% of variation in Resale value(Y) is exaplined by the Bus mileage(X)