Lecture 06 - PAM 3300 Regression Analysis Evaluating the...

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PAM 3300: Regression Analysis
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Evaluating the model: R 2 A useful summary of how well a model predicts the actual outcomes is R 2 : R 2 = Var(Yhat)/Var(Y) = 1-Var(residuals)/Var(Y) This is just the square of the correlation between Y and Yhat. Measures the proportion of the variation in Y that is explained by the regression model. This measures how well the model fits the data, but nothing more.
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Evaluating the model: Examples of R 2 R 2 =.804 High R 2 : Model explains the data well.
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Evaluating the model: Examples of R 2 R 2 =.144 Low R 2 : Model fits the data poorly.
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Evaluating the model: R 2 to choose best descriptive model R 2 =.175 R 2 =.145
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Inference in regression analysis Given a sample of N people randomly drawn from a population, we can compute an estimate of b. In general, we are interested in whether the effect of X on Y is different from zero (or some other hypothesized value) - we want to infer from our evidence (estimate of b) whether this is true. For any given sample, b is likely to be different from zero. But before concluding that X has an effect on Y, we want to be sure this wasn’t the result of random chance. To decide whether b is different from zero in a ‘statistically significant’ sense we need to know how b compares to the ‘sampling distribution’ of b.
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Sampling Distribution of b For every sample of size N that we could draw from the population, we would compute a different b. We can figure out the sampling distribution under the ‘null hypothesis’ that the ‘true’ value of b is b* (e.g., zero).
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