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Lecture7_2005

# Lecture7_2005 - Statistics Professor Green Perils of...

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Statistics Professor Green Perils of Multiple Regression Least-squares regression rests on several assumptions about the causal process by which the data were generated. Becoming an intelligent consumer of statistical information requires one to understand each assumption and how the results may be distorted if it is violated. A. The independent variables are statistically independent of the disturbances. This assumption implies, among other things, that (1) no omitted predictors of Y are correlated with X and (2) causation flows in just one direction from X —> Y. B. The independent variables are measured without error. C. Each of the disturbances is drawn from the same underlying distribution. Thus, disturbances are expected to have the same variance from one observation to the next. D. Each disturbance is statistically independent of all other disturbances. Violations of (A) and (B) are potentially very serious: biased and possibly misleading regression slopes, standard errors, and regression diagnostics. Violations of (C) and (D) result in biased standard errors and therefore inaccurate confidence intervals or hypothesis tests. To fix ideas, let’s consider an example based loosely on the notorious Bell Curve . In that book, the authors argued that race affected incomes, even after controlling for education. The political implications of their argument were, and remain, quite explosive. The results were based on young people who had been surveyed in high school and tracked as they entered the labor market thereafter. For the sake of exposition, I have simplified the data analysis, while keeping the basic patterns of the data intact. Here are the independent variables. First, race is coded 0 for whites and 1 for nonwhites. Tally for Discrete Variables: RACE RACE Count Percent 0 367 73.40 1 133 26.60 N= 500 Education is measured by years of schooling. Clearly, this is a sloppy measure of educational attainment (warming a chair does not an education make). For the sake of the example, imagine

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