Jaymie Ticknor Quantitative Methods 2317 Sect 001 23 and 25 April 2014 Prediction Chapter 12 Lecture 12 Predict scores on one variable based on scores from one or more variables Correlation does not matter which variable is which Prediction have to designate which variable is the predictor variable X and which variable is being predicted criterion Y variable Mean is best predictor a b X person s predicted score on criterion variable a regression constant b unstandardized regression coefficient slope X person s score on predictor variable Use a prediction equation we draw a line called a regression line that runs through the points on our scatter diagram Slope of regression line amount line moves up for every unit it moves across regression coefficient b Intercept of regression line point at which line crosses the vertical access Y intercept regression constant a Determining the Regression Equation and Line Come up with the line that minimizes the error between The predicted score on the criterion variable Actual score on the criterion variable Want least amount of error total over all the predicted scores smallest sum of squared errors Some errors are positive actual point is above regression line Some errors are negative actual point is below the regression line b X MX Y MY SSX a MY b MX Standardized Regression Coefficient researchers sometimes use different measures or the same measure with a different scale results from our regression equation and line would not compare because the scale of the predictor and criterion variables affect the regression coefficient b So need to standardize the regression coefficient by using b SSX SSY When we have one predictor variable the standardized regression coefficient beta has the same value as the correlation coefficient r between the two variables Multiple Regression predict a person s score on a criterion variable from one predictor variable called linear bivariate regression bivariate means two variables Can also predict a person s score on a criterion variable from more than one predictor variable called multiple regression a b1 X1 b2 X2 In multiple regression the for any predictor will usually be less than the r between the predictor and criterion variable The in multiple regression refers to that predictor s unique relationship with the criterion variable taking into account the other predictor variables there is usually an overlap among predictor variables Multiple correlation coefficient R correlation between the criterion Y variable and all predictor X variables Squared multiple correlation R2 amount of variance in the criterion Y variable that is accounted for by all predictor X variables proportion of variance in DV is explained by the IVs Hypothesis Testing in Multiple Regression Two different hypothesis tests Significance of multiple correlation are both predictor variables related to criterion variable Significance of each individual predictor Limitations of Prediction Same as correlation Curvilinear relationship Restriction of range coefficient is changed compared to original coefficient Unreliability of measures reliability scores measured are consistent validity measuring what concept you are suppose to measure Outliers when adding outliers coefficient changes strength of correlation Causality direction of causality Controversy Unstandardized versus Standardized Regression Coefficient Some things to consider Theoretical vs Applied Comparing predictors different variables on different scales can compare if standardized Meaningful units