Regression - University of North Texas College of ….ppt

KNN Ch. 2 Inferences in Simple Linear Regression;Normal Error Regression Model;Inferences About ?1 -- The Slope of the Regression Line;Usual inference about ?1;Slope of the regression line is 0; There is no linear relationship between X and Y; Regression line is horizontal Means of probability distributions for all Yi are equal: Probability distributions of all Yi are identical;Required Test Statistic for Evaluating Ho;Estimating ;Estimating s{b1} for GMAT Example;;;For GMAT Example;Two-Sided (Tailed) Test of HoGMAT Example;Decision Rule for Test of Ho;;IBM SPSS Results...;A One-Sided (Tailed) Test of ?1;Decision Rules;For the GMAT Data...;ANOVA Approach to Regression;Essentially...;Sums of Squares are Additive;The ANOVA Table;GMAT Example..;GMAT ANOVA Table;IBM SPSS ANOVA;The F-test for the ANOVA..;Relationship Between F and t;General Linear Test Approach;Approach Involves...;Test Statistic;Coefficient of Determination;GMAT Example;Measures of Strength of Association;Correlation Coefficient;Correlation Coefficient;Relationship Between r and b1;Limitations of r r2;Limitations of r r2;When X and Y are standardized When X and Y are in raw score form (non-standardized) . ; Is rxy a least squares estimator or an MLE estimator? Is this estimator unbiased? What is it an “estimator” of ? Isn’t this the same as “r” from a simple linear regression model? Point Biserial “r” (one variable dichotomous) ;Formulae for r;Inferences on Correlation Coefficients;Advance Inference on Correlation Coefficient; Interval Estimation of rXY Sampling distribution of rXY is complicated when rXY? 0 Cannot use “t” ! If n ? 25 then where, When n ? 25, ;Estimation of rXY (Continued.) Then the CI for is, We have to retransform back to rXY in order to get its CI. See KNN for testing hypotheses about independent samples from two bivariate normal populations ; What if populations are not Normal? Resort to non-parametric approach The famous Spearman “Rank” Correlation