Question

The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. a sample of buses resulted in the following data. click on the datafile logo to reference the data.

age of bus (years) maintenance cost ($)
1 350
2 370
2 480
2 520
2 590
3 550
4 750
4 800
5 790
5 950
Use the data to develop an estimated regression equation that could be used to predict the annual maintenance cost given the age of the bus. What is the estimated regression model?

Answer 1

To estimate the regression equation for predicting annual maintenance cost based on the age of the bus, the process involves plotting the data, calculating the least-squares regression line, determining the correlation coefficient for significance, and using the regression equation for predictions.

Step-by-step explanation:

To develop an estimated regression equation for predicting annual maintenance cost based on the age of the bus, we follow the steps for simple linear regression:

1. Plot the data with the age of the bus on the x-axis and the maintenance cost on the y-axis to get a scatter plot.
2. Calculate the least-squares regression line using the formula ý = a + bx, where a is the y-intercept, b is the slope, x is the age of the bus, and ý is the predicted annual maintenance cost.
3. Compute the correlation coefficient to assess the strength and direction of the linear relationship.
4. If needed, test the significance of the correlation coefficient to determine if the relationship between age and cost is statistically significant.
5. Predict costs for specific ages using the regression equation.

To find the slope (b) and intercept (a), we'll use statistical software or detailed calculations involving the sum of the products of the deviations of x and y from their means, divided by the sum of the squared deviations of x from its mean. The slope (b) will provide information on how much the maintenance cost increases for each additional year of bus age. Once we determine the slope and the y-intercept, we would write the equation in the form, ý = a + bx.

Note: Actual calculations of the slope, intercept, and correlation coefficient are not included since the necessary data for computations (sums of squares, products of deviations) are not provided in the question.