916666 Var(y) = 5. 83333 Cov(xy) = 2. 91666 ??;cccccc cc$?V ????? Correlation??ZMeasures the relative strength of the linear relationship between two variables Unit-less Ranges between 1 and 1 The closer to 1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker any positive linear relationship?BPZ?x&#??????;Scatter Plots of Data with Various Correlation Coefficients?<P<?? ?n???Linear Correlation?? ?o???Linear Correlation?? ?p???Linear Correlation?? ?? ??(Calculating by hand& ?? ?????8Simpler calculation formula& ?? ?(???2Sampling distribution of correlation coefficient: ? 32 ??*note, like a proportion, the variance of the correlation coefficient depends on the correlation coefficient itself??substitute in estimated r ?P?ZZs"?"?g???Sample size requirements for r?? ????Correlation in SAS??/*To get correlations between variables 1 and 2, 1 and 3, and 2 and 3:*/ PROC CORR data=yourdata; var variable1 variable2 variable3; run; /*To get correlations between variables 3 and 1 and 3 and 2:*/ PROC CORR data=yourdata; var variable1 variable2; with variable3; run; ?ZI3?f? ?3?f? ?PXt-?????Linear regression?? ????"What is Linear ???Remember this: Y=mX+B???????What s Slope????? Prediction??If you know something about X, this knowledge helps you predict something about Y. (Sound familiar?& sound like conditional probabilities?) ?4?? " 2??? ??(Regression equation& ?? ????2 Recall example: cognitive function and vitamin D ?33(???Hypothetical data loosely based on [1]; cross-sectional study of 100 middle-aged and older European men. Cognitive function is measured by the Digit Symbol Substitution Test.