Question

3. 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 sample linear regression line. You need to decide which one is the dependent 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 plain English.

Answer 1

(a) y = 126.5 - 12.875*x

(b) For every additional bus mileage, the market resale value of the bus will decrease by 12.875.

(c) The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

(d) The value of the coefficient of determination is 0.884.

88.4% of the variability in the model is explained.

Data				Forecasts and Error Analysis
Period	Demand (y)	Period(x)		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	58	5		62.125	-4.125	4.125	17.01563	07.11%
Period 2	90	3		87.875	2.125	2.125	4.515625	02.36%
Period 3	85	4		75	10	10	100	11.76%
Period 4	96	2		100.75	-4.75	4.75	22.5625	04.95%
Period 5	64	5		62.125	1.875	1.875	3.515625	02.93%
Period 6	57	5		62.125	-5.125	5.125	26.26563	08.99%
				Total	0	28	173.875	38.11%
Intercept	126.5			Average	0	4.666667	28.97917	06.35%
Slope	-12.875				Bias	MAD	MSE	MAPE
						SE	6.593083
Forecast	36.375	7
						Correlation	-0.94026
						Coefficient of determination	0.884083