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# 16 Regression - 1 PSYC110 Regression(Part II Today’s Outline Basic review of correlation and regression Including partial formula sheet

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Unformatted text preview: 3/25/2008 1 PSYC110 MARCH 25, 2008 Regression (Part II) Today’s Outline Basic review of correlation and regression Including: partial formula sheet Quantifying errors of prediction “Standard error of the estimate” Numeric example Correlation and Regression So Far Correlation Linear association between any two variables Continuous data! (ordinal, interval, or ratio scale) r quantifies the association (- 1.00 ≤ r ≤ +1.00) Assumptions Linear relationship Both X and Y normally distributed (fairly robust to violating) Equal variance of Y across the range of X (fairly robust to violating) Covariance = non-standardized association (units matter) Correlation = standardized association (units don’t matter) 3/25/2008 2 Correlation and Regression So Far Simple Regression Predicting one criterion variable Y from one predictor var. X Y = actual values, Y-hat ( ) = predicted values Best-fitting regression line: Minimizes sum of squared distances between actual and predicted Y values… in notation: minimizes (Y minus Y-hat) 2 Find regression line: use formulas for a (intercept) and b (slope) Draw regression line: plot any two points and draw a line through To plot a point: plug X into regression equation, calculate Y-hat Cannot infer causality from either correlation or regression ? Correlation/Regression Formula Sheet (So Far) Statistic / coefficient / concept Symbol Formula Covariance cov XY Correlation r Regression equation (not applicable) Slope b Intercept a ? ?? = ¡¢? − ? £ ¤ ( ? − ? £ ) − 1 ¥ = ? ?? ¦ ? ¦ ?...
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## This note was uploaded on 05/05/2008 for the course PSYCH 110 taught by Professor Burt during the Spring '08 term at Vermont.

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16 Regression - 1 PSYC110 Regression(Part II Today’s Outline Basic review of correlation and regression Including partial formula sheet

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