BIVARIATE REGRESSION AND CORRELATION

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Presentation transcript:

BIVARIATE REGRESSION AND CORRELATION WHY AND WHEN TO USE REGRESSION/CORRELATION? WHAT DOES REGRESSION/CORRELATION MEAN?

You should be able to interpret: The least squares equation. R2 and Adjusted R2 F and significance. The unstandardized regression coefficient. The standardized regression coefficient. t and significance. The 95% confidence interval. A graph of the regression line.

ASSUMPTIONS UNDERLYING REGRESSION/CORRELATION NORMALITY OF VARIANCE IN Y FOR EACH VALUE OF X For any fixed value of the independent variable X, the distribution of the dependent variable Y is normal. NORMALITY OF VARIANCE FOR THE ERROR TERM The error term is normally distributed. (Many authors argue that this is more important than normality in the distribution of Y). THE INDEPENDENT VARIABLE IS UNCORRELATED WITH THE ERROR TERM

ASSUMPTIONS UNDERLYING REGRESSION/CORRELATION (Continued) HOMOSCEDASTICITY It is assumed that there is equal variances for Y, for each fixed value of X. LINEARITY The relationship between X and Y is linear. INDEPENDENCE The Y’s are statistically independent of each other.