For this assignment, you will use the “Trucks” dataset. You will use SPSS to analyze the dataset and address the questions presented. Findings should be presented in a Word document along with the SPSS outputs.
The business characteristics of n = 250 U.S. trucking and delivery companies for calendar year 2011 were recorded. Among the characteristics studied were the number of drivers and the number of trucks (power units) each company employed.
Given that the data consists of counts and range of counts is large, a natural log transformation is usually performed to improve the linear model results. Apply a natural log transform to both variables and then plot the Y = log(Trucks) vs. X = log(Drivers).
Is there a linear relationship? Justify your answer by providing the SPSS output as an illustration.
Build a simple linear model by regressing Y on X and testing whether or not a relationship exists between the number of drivers and the number of trucks. Address the following questions in your written response:
- After fitting the model, plot the standardized residuals (on vertical axis) vs. the standardize predictions (on horizontal axis). Is there a pattern? How would you interpret the pattern or lack of pattern?
- After fitting the model, derive the normal probability plot and interpret what the plot means.
- What is the coefficient of determination, R2, of the model? How would you interpret the R2?
- What is the estimate of ß1? How would you interpret the estimate of ß1?
- Is the estimate of ß1 significantly different than 0? Assume an a = 0.01.
- What is a 95% confidence interval for ß1? How would you interpret the 95% confidence interval for ß1?
- If a new trucking and delivery company with 4,900 drivers were to be formed, how many trucks would you expect the company would employ based on the model?