国外社会科学统计课件regression.ppt

Statistics for the Social Sciences Psychology 340 Fall 2006 Outline (for week) Simple bi-variate regression, least-squares fit line The general linear model Residual plots Using SPSS Multiple regression Comparing models, (?? Delta r2) Using SPSS Regression Last time: with correlation, we examined whether variables X Y are related This time: with regression, we try to predict the value of one variable given what we know about the other variable and the relationship between the two. Regression Last time: “it doesn’t matter which variable goes on the X-axis or the Y-axis” Regression Last time: “Imagine a line through the points” The equation for a line A brief review of geometry The equation for a line A brief review of geometry The equation for a line A brief review of geometry Regression A brief review of geometry Consider a perfect correlation Regression Consider a less than perfect correlation Regression The “best fitting line” is the one that minimizes the error (differences) between the predicted scores (the line) and the actual scores (the points) Regression The linear model Scatterplot From the Computing Pearson’s r lecture Computing regression line(with raw scores) Computing regression line(with raw scores) Computing regression line (with raw scores) Computing regression line(standardized, using z-scores) Computing regression line(standardized, using z-scores) Prediction model Predicted Z score (on criterion variable) = standardized regression coefficient multiplied by Z score on predictor variable Formula Computing regression line(with z-scores) Regression Also need a measure of error Regression Error Actual score minus the predicted score Measures of error r2 (r-squared) R-squared r2 represents the percent variance in Y accounted for by X Computing Error around the line Compute the difference between the predicted values and the observed values (“residuals”) Computing Error around the line Computing Error around the line Computing Error around the l