ECON7300
Statistical Project: Part IIIb
Semester 1, 2024
Instructions
• Questions in this file should be answered by students whose last names fall within the range X-Z.
• Use the Excel file Part3b_Dataset3 to answer the questions.
• A 100% penalty will apply if your answers are not based on the questions and datasets assigned to your lastname.
Multiple Regression Analysis
The following information was collected for a random sample of 118 house sales in Massachusetts in the United States in 1981: house price, house size, house age, and whether the house is located near a garbage incinerator. The variables in the provided dataset (Part3b_Dataset3) are:
• price (Y, house price in thousands of US dollars)
• area (X1, size of house in square feet)
• age (X2, age of house in years)
• nearinc (X3, coded 1 if the house is within three miles of a garbage incinerator and 0 if the house is further than three miles from a garbage incinerator)
The dependent variable for your analysis is price.
Answer the following questions using Part3b_Dataset3.
(a) Estimate a regression model using X1 and X2 to predict Y. Include the regression output and state the multiple linear regression equation.
(b) Interpret the meaning of each of the slope coefficients.
(c) Predict Y when X1 = 3000 and X2 = 25.
(d) Construct a 95% confidence interval estimate of themeanY for all house sales in Massachusetts in 1981 when X1 = 3000 and X2 = 25, and interpret its meaning.
(e) Construct a 95% prediction interval of Y for a house sale in Massachusetts in 1981 when X1 = 3000 and X2 = 25, and interpret its meaning.
(f) Perform. a residual analysis by analysing the relevant residual plots. Is there any evidence that the regression assumptions have been violated? Explain your answers.
(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? Explain your answer.
(h) At the 5% level of significance, use t tests to determine whether each independent variable (X1 and X2) makes a significant contribution to the regression model. Follow all the necessary steps. Based on these results, suggest which independent variables should be included in the model.
(i) Test for the significance of the overall multiple regression model with two independent variables (X1 and X2) at the 5% level of significance. Follow all the necessary steps.
(j) Use partial F tests to determine whether there is a significant relationship between Y and each independent variable (X1 and X2) at the 5% level of significance. Follow all the necessary steps.
(k) Compute the coefficients of partial determination of the multiple regression model with two independent variables (X1 and X2) and interpret the meaning of each coefficient of partial determination.
(l) Estimate a regression model using X1, X2 and X3 to predict Y. Include the regression output and state the multiple linear regression equation, the regression equation for houses near an incinerator, the regression equation for houses that are not near an incinerator, 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. Include the regression output and state the multiple linear regression equation.
(n) Test the joint significance of the three interaction terms using a partial F test to determine if the interaction terms significantly improve the regression model. Assume a 5% level of significance. Follow all the necessary steps. If you reject the null hypothesis, you also need to test the contribution of each interaction term separately (using partial F tests) to determine which interaction terms to include in the model).