代做ECON7300 Statistical Project: Part II Semester 1, 2024帮做R语言

日期：2024-05-02 03:45

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ECON7300

Statistical Project: Part II

Semester 1, 2024

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), aresearcher 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 themeanY 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.