Internal Code: 1HAIJ
Instructions for Dataset 1: Simple Regression Analysis
A critical factor for used-car buyers when determining the value of a car is how far the car has been driven. To examine this issue, a used-car dealer randomly selected 90 five-year-old Ford Lasers that has been sold at auctions during the past month. The dealer recorded the price and the number of kilometers on the odometer.
The data file dataset1.xls contains data of 90 cars and the variables in the dataset are:
1. Price (Y, action selling price in $’000)
2. Odometer (X, Odometer reading in ‘000 km)
The dependent variable for your analysis is Price.
Answer the following questions using dataset 1.
(a) Create a scatter plot of Y on the vertical axis against X on the horizontal axis (make sure to label each axis).
(b) Using the scatter plot in (a), does there appear to be a relationship between Y and X? If so, in what direction is the relationship? How strong is the relationship?
(c) Estimate a simple regression model using X to predict Y (present the output and write out the estimated equation).
(d) Interpret the intercept coefficient. Does it make sense?
(e) Interpret the slope coefficient.
(f) Compute the coefficient of determination and interpret its meaning.
(g) Compute the standard error of the estimate and interpret its meaning. Judge the magnitude of the standard error of the estimate.
(h) Perform a residual analysis (plot the residuals) and evaluate whether the assumptions of regression have been violated.
(i) Test for the significance of the slope coefficient using t test (follow all the necessary steps). Assume 5% level of significance.
(j) Test for the slope using F test (follow all the necessary steps). Assume 5% level of significance.
(k) Compute a 95% confidence interval estimate of the mean Y for all cars when X = 30 and interpret its meaning.
(l) Compute a 95% prediction interval of Y for a single car when X = 30 and interpret its meaning.
Instructions for Dataset 2: Multiple Regression Analysis
The data file dataset2.xls is an extract of the U.S. Census Bureau’s Current Population Survey on American workers. A random sample of 490 workers are taken.
The variables in the dataset are:
The dependent variable for your analysis is Salary.
Answer the following questions using dataset 2.
(a) Estimate a regression model using Education and Age to predict Salary (present the output and write out the estimated equation).
(b) Interpret the slope coefficients.
(c) Predict Salary when Education = 20 and Age = 55. Comment on this prediction.
(d) Plot the residuals to test the assumptions of the regression model. Is there any evidence of violation of the regression assumptions? Explain.
(e) Determine the variance inflation factor (VIF) for each independent variable (Education and Age) in the model. Is there reason to suspect the existence of collinearity?
(f) Are all individual variables significant at the 5% level? Use t tests and follow all the necessary steps.
(g) Test for the significance of the overall multiple regression model at 5% level of significance.
(h) Estimate a regression model using Education, Age and Female to predict Salary (present the output, and write out the multiple regression equation, the regression equation for male workers and the regression equation for female workers). Interpret the coefficient for Female.
(i) Test the hypothesis that there is wage discrimination against women at the 5% level.
(j) Estimate a regression model using Education, Age, Female, and an interaction between Female and Education to predict Salary (present the output and write out the estimated equation). Interpret the coefficients of Education and the interaction term.
(k) Test whether the return to education is the same for women and men at the 5% level.
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