ECON7300: Statistical Project Assignment (Part IIIb), Semester 1, 2023
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ECON7300: Statistical Project Assignment (Part IIIb), Semester 1, 2023
Instruction:
(A) Questions in this paper should be answered by students whose surnames fall within the range G-M.
(B) Use the Excel file ‘Dataset2_part3b to answer the questions asked.
(C) A heavy penalty will be applied if your answers are not based on dataset assigned to you.
Instructions for Dataset2_part3b: Multiple Regression Analysis
A random sample of 450 academic staff working in country W were interviewed and the following information was collected (and saved in Dataset2_part3b): academic year salary in dollars; number of years in rank, years since obtaining first degree; and gender.
The variables saved in Dataset2_part3b are:
• sal (Y, academic year salary in dollars)
• nyr (X1, number of years in rank)
• nyd (X2, number of years since obtaining first degree)
• gender (X3, coded 1 for male academic staff and 0 for female academic staff) The dependent variable for your analysis is sal.
Answer the following questions using Dataset2_part3b
(a) Estimate a regression model using X1 and X2 to predict Y (state the multiple regression equation).
(b) Interpret the meaning of the slopes.
(c) Predict Y when X1 = 14 and X2 = 25.
(d) Compute a 95% confidence interval estimate of the mean Y for all academic staff working in country W when X1 = 14 and X2 = 25 and interpret its meaning.
(e) Compute a 95% prediction interval of Y for an academic staff working in country W when X1 = 14 and X2 = 25 and interpret its meaning.
(f) Plot the residuals to test the assumptions of the regression model. Is there any
evidence of violation of the regression assumptions? Explain.
(g) Determine the variance inflation factor (VIF) for each independent variable (X1 and X2) in the model. Is there reason to suspect the existence of collinearity? Why?
(h) At the 0.05 level of significance, determine whether each independent variable (X1 and X2) makes a significant contribution to the regression model (use t tests and follow all the necessary steps). On the basis of these results, indicate the independent variables to include in the model.
(i) Test for the significance of the overall multiple regression model (with two independent variables, X1 and X2) at 5% level of significance.
(j) Determine whether there is a significant relationship between Y and each
independent variable (X1 and X2) at the 5% level of significance (hint: testing portions of the multiple regression model using the partial F test).
(k) Compute the coefficients of partial determination for a multiple regression model containing X1 and X2 and interpret their meaning.
(l) Estimate a regression model using X1, X2 and X3 to predict Y (state the multiple regression equation, the regression equation for male academic staff working in country W, the regression equation for female academic staff working in country
W) and interpret the coefficient for X3.
(m) Estimate a regression model using X1, X2, X3, an interaction between X1 and X2, an interaction between X1 and X3, and an interaction between X2 and X3 to predict Y.
(n) Test whether the three interactions significantly improve the regression model. Assume 5% level of significance (hint: test the joint significance of the three interaction terms using the partial F test. If you reject the null hypothesis, test the contribution of each interaction separately (using the partial F test) in order to determine which interaction terms to include in the model).
2023-05-06