Simple Regression Analysis

/in /by

Details:

The purpose of this assignment is to apply simple regression
concepts, interpret simple regression analysis models, and justify
business predictions based upon the analysis.

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.

Part 1:

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.

Part 2:

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:

  1. 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?
  2. After fitting the model, derive the normal probability plot and interpret what the plot means.
  3. What is the coefficient of determination, R2, of the model? How would you interpret the R2?
  4. What is the estimate of β1? How would you interpret the estimate of β1?
  5. Is the estimate of β1 significantly different than 0? Assume an α = 0.01.
  6. What is a 95% confidence interval for β1? How would you interpret the 95% confidence interval for β1?
  7. 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?

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Please review the rubric prior
to beginning the assignment to become familiar with the expectations
for successful completion.