Statistics for Business and Economics

A car dealer is investigating whether there is any relationship between a car price and its weight. He gathered data on weight (in pound) and price (in dollar) of a random sample of 150 cars.
The variables in the dataset are:
 Price (in dollar)
 Weight (in pound)
The dependent variable for your analysis is Price.
Answer the following questions using dataset 1.
(a) Estimate a regression model using weight to predict car price (state the simple linear regression equation).
(b) Interpret the meaning of the slope.
(c) Predict price when weight = 3200.
(d) Compute the coefficient of determination and interpret its meaning.
(e) Compute the standard error of the estimate and interpret its meaning. Judge the magnitude of the standard error of the estimate.
(f) Perform a residual analysis (plot the residuals) and evaluate whether the assumptions of regression have been violated.
(g) Test for the slope using t test (follow all the necessary steps). Assume 5% level of significance.
(h) Test for the slope using F test (follow all the necessary steps). Assume 5% level of significance.
(i) Test for the correlation coefficient (follow all the necessary steps). Assume 5% level of significance.
(j) Compute a 95% confidence interval estimate of the mean car price in the population when weight = 3200 and interpret its meaning.
(k) Compute a 95% prediction interval of a single car price with weight = 3200 and interpret its meaning.
Statistical Project Assignment, Semester 2, 2014

Instructions for Dataset 2: Multiple Regression Analysis (45 marks)
The data considered here are a subset comprising n = 495 of the faculty members provided by DeMaris (2004). DeMaris analysed data on the salary of faculty (academic staff) at Bowling Green State University in Ohio, USA in the academic year 1993-1994.
The variables in the dataset are:
 salary (academic year salary in US dollar)
 exprior (number of years of prior experience)
 yearsrank (number of years in rank)
 gender(1 for male faculty member and 0 for female faculty member)
The dependent variable for your analysis is salary.
Answer the following questions using dataset 2.
(a) Estimate a regression model using number of years of prior experience (exprior) and number of years in rank (yearsrank) to predict salary (state the multiple regression equation).
(b) Interpret the meaning of the slopes.
(c) Predict salary when exprior = 16 and yearsrank = 20.
(d) Compute a 95% confidence interval estimate of the mean salary in the population when exprior = 16 and yearsrank = 20 and interpret its meaning.
(e) Compute a 95% confidence interval estimate of salary for an individual with exprior = 16 and yearsrank = 20 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 (exprior and yearsrank) in the model. Is there reason to suspect the existence of collinearity?
(h) At the 0.05 level of significance, determine whether each independent variable 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 at 5% level of significance.
Statistical Project Assignment, Semester 2, 2014
(j) Determine whether there is a significant relationship between salary and each independent variable 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 and interpret their meaning
(l) Estimate a regression model using exprior, yearsrank and gender to predict salary (state the multiple regression equation, the regression equation for male academic staff, the regression equation for female academic staff) and interpret the coefficient for gender.
(m) Estimate a regression model using exprior, yearsrank, gender, an interaction between exprior and yearsrank, an interaction between exprior and gender, and an interaction between yearsrank and gender to predict salary.
(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).

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