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Published byIrene Hubbard Modified over 9 years ago
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Multiple Linear Regression
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Purpose To analyze the relationship between a single dependent variable and several independent variables
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Key terms Bivariate Partial Correlation: Simple correlation between two variables after the effects of all other variables is removed Correlation: how a change in one variable affects another variable Strength Direction Dependent variable: criterion Independent variable: predictor
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Key terms Regression variate: a linear combination of the independent variables used to attempt to predict the dependent variable Beta coefficient: standardized regression coefficient that allows for a direct comparison between variables as to their relative explanatory power of the dependent variable
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Key Terms Correlation Coefficient R: degree to which two or more predictors are related to the criterion. Measure applied to the variate. Coefficient of determination R square: Measure of the proportion of the variance of the criterion that is explained by the predictors. Measure applied to the variate.
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Key terms Residual Variance and R-square. This value is immediately interpretable in the following manner. If we have an R-square of 0.4 then we know that the variability of the Y values around the regression line is 1-0.4 times the original variance; in other words we have explained 40% of the original variability, and are left with 60% residual variability. Ideally, we would like to explain most if not all of the original variability. The R-square value is an indicator of how well the model fits the data (e.g., an R-square close to 1.0 indicates that we have accounted for almost all of the variability with the variables specified in the model).
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Steps First interpret the variate. If the variate is NOT significant, stop. If it is significant, then you can interpret the Betas and R square values. Use the Betas to answer your hypotheses.
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