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# "multicollinearity" problem

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Suppose you want to estimate a model of women's earnings at age 50. You have data for a sample of employed women, provided by the alumni associations of Mills College and Smith College, on:
? A woman's salary at age 50
? Her age
? Year of graduation
? Her high school GPA
? Her college GPA
? Her college major
? Her job tenure (how many years she has been with employer)
? The fraction of her household income that she earns
The question below violate assumptions of the classical model

1.Say that your regression results include a large, positive coefficient on ECON MAJOR, and you tell all your fellow students about it. Why might this coefficient be an overestimate of the average gain in future salary that your fellow students should expect just by switching their major to economics?

2. If you notice that virtually all the Econ majors in your sample are from Mills College, what problem will you have with the following regression model?
SALARY= &#946;0 + &#946;1 COLLEGE GPA + &#946;2 MILLS GRAD + &#946;3 ECON MAJOR + &#949;

3.Suppose that you run two versions of your model. In the first, SALARY is expressed in thousands of dollars. In the other, it is expressed in dollars. Will this affect the size of your coefficients? The size of the standard errors? The adjusted R2? Explain

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#### Solution Preview

1. Apparently, this question has more to do with economic theory rather than econometrics. The reason why this coefficient might be an overestimate of the future salary if you tell all your fellows about it is that the supply of people with a major in Economics will increase, thereby lowering the equilibrium wage that firms will pay to higher them. In other words: the result of the regression tells you that, currently, people with a major in Economics are earning a high salary. Now, if you tell everybody about this finding, many people will start studying Economics. Therefore, in the future there will be more people with Economics studies, and if demand for them does not increase, their price (ie, the salary) will tend to fall. We conclude that the fact that people with a major in Economics are earning high salaries today (which what the regression tells us) doesn't necessarily imply ...

#### Solution Summary

Investigate a "multicollinearity" problem is determined.

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## Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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