Question

A regional transit company wants to determine whether there is a relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the following data:

Age of Bus (years)	Annual Maintenance Cost ($)
1	350
2	370
2	480
2	520
2	590
3	550
4	750
4	800
5	790
5	950

Instructions:

1. Input the data into an SPSS work sheet making sure that all your variables are labelled appropriately
2. Create a scatter plot for these data.
3. What does the scatter plot indicate about the relationship between the age of a bus and its annual maintenance costs?
4. What is the correlation coefficient between the age of a bus and annual maintenance cost?
5. Estimate a regression model that could be used to predict the annual maintenance cost given the age of the bus.
6. What is the equation of the estimated model?
7. Test whether each of the regression parameters β₀ and β₁ is equal to zero at the 0.05 level of significance testing.
8. What is the correct interpretations of these parameters?
9. How much of the variation in the sample values of annual maintenance costs does the regression model you estimated explain?
10. What do you predict the annual maintenance cost to be for a 4.5 year old bus?

Answer 1

Answer:

A regional transit company wants to determine whether there is a relationship between the age of a bus and the annual maintenance cost.

A sample of 10 buses resulted in the following data:

Age of Bus (years)	Annual Maintenance Cost ($)
1	350
2	370
2	480
2	520
2	590
3	550
4	750
4	800
5	790
5	950

(a).

SPSS OUTPUT:

Scatter diagram:

From the above scatter diagram we can observe that the points are scattered from lower left corner to upper right corner.

It indicates that there was a positive correlation between the given two variables,

(b).

Correlations
		Age of a Bus	Annual Maintenance Cost
Age of bus	Pearson Correlation	1	0.934
	Sig.(2-tailed)		0.000
	N	10	10
Correlation is significant at the 0.01 level (2-tailed)

The correlation coefficient between the age of a bus and annual maintenance cost is (r) = 0.934

(c).

Coefficients
Model		Unstandardized Coefficients		Standardized Coefficient	t	Sig.
		0	Std.Error	Beta
1	(Constant)	220.000	58.481		3.762	0.006
	Age of a bus	131.667	17.795	0.934	7.399	0.000
	a. Dependent Variable: Annual maintenance cost

The estimated regression equation is Y = 220 + 131.666 X

(d).

From the above table we can observe that both β0 and β1 are different from zero (both the p values are <0.005).

Slope interpretation: One unit change in age of a bus the annual maintenance cost was increased by 131.667 dollars.

(e).

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	0.934a	0.873	0.857	75.498
a. Predictors : (Constant). Age of a bus

From the above table we can observe that R₂ = 0.873,

i.e. 87.3% of variation in the annual maintenance cost is explained by age of a bus only.

(f).

If x = 4.5 years then y = $812.5015