ECON7300 Statistical Project: Part II Semester 2, 2023
1
ECON7300
Statistical Project: Part II
Instructions
 Questions in this file should be answered by students whose last names fall
within the range X-Z.
 Use the Excel file Part2_Dataset3 to answer the questions.
 A 100% penalty will apply if your answers are not based on the questions and
datasets assigned to your last name.
ECON7300 Statistical Project: Part II Semester 2, 2023
2
Simple Regression Analysis
To study the relationship between participation in a pension plan (prate) and the plan’s generosity as
measured by the match rate (mrate), a researcher samples 1,534 pension plans in the United States.
The variables in the dataset (Part2_Dataset3) are:
• prate (Y, in percentage of employees with the pension plan)
• mrate (X, in cents of average company contribution to the employee’s pension fund for each
dollar the employee contributes; for example, a value of 0.6 means the company contributes
60c to the pension plan for every $1 contribution by the employee)
The dependent variable for your analysis is prate.
Answer the following questions using Part2_Dataset3.
(a) Estimate a regression model using X to predict Y. Include the regression output and state the
simple linear regression equation.
(b) Interpret the meaning of the slope coefficient.
(c) Predict Y when X = 1.
(d) Compute the coefficient of determination and interpret its meaning.
(e) Compute the standard error of the estimate, interpret its meaning, and judge the magnitude
of the standard error of the estimate.
(f) Perform a residual analysis by analysing the relevant residual plots to evaluate whether the
regression assumptions have been violated.
(g) Complete the t test for the slope, following all the necessary steps. Assume a 5% level of
significance.
(h) Complete the F test for the slope, following all the necessary steps. Assume a 5% level of
significance.
(i) Complete the test for the correlation coefficient, following all the necessary steps. Assume a
5% level of significance.
(j) Construct a 95% confidence interval estimate of the mean Y when X = 1 for all pension
plans in the United States, and interpret its meaning.
(k) Construct a 95% prediction interval of Y when X = 1 for a pension plan in the United States
and interpret its meaning.