CHAPTER 6 - CHAPTER 6 REGRESSION Higher correlations...

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CHAPTER 6: REGRESSION Higher correlations between the independent and dependent variables lead to better predictions For r=-1 or +1, the dependent variable, Y, can be predicted with perfect accuracy from the  independent variable, X. For r=0, knowledge of X is useless in predicting Y Predictions are made using regression analysis Regression analysis-  applies to paired data(X i  , Y i ) where X is the independent variable with  values X that are selected in advance and Y is the dependent variable with values Y i  that are  free to vary. However, regression procedures also are applicable when both X and Y are free to  vary, as they are in correlation. Can improve predictions by using more than one predictor Multiple regression-  simultaneous use of 2 or more predictors in predicting a dv Overview of Prediction Process Predictions based on small samples tend to be unstable in that they vary from sample to  sample. Improve predictions by using all the data instead of a small subset. Predictions based on the regression line take into account all the sample data and are more  stable than those based on only the mean of the Y scores corresponding to a given X score. Both procedures presuppose that the population represented by the current sample does not  differ from that represented by the earlier sample. Regression approach assumes the data points have been fitted by the correct regression  equation. Check this by looking at the scatterplot. 6.2 Criterion for the Line of Best Fit Predicting Y from X The best-fitting line should minimize some function of the error in predicting Y i  from X i   Prediction error or residual - e , defined to be the difference between the ith person’s actual  score, Y i  , and the score predicted for that personY i ’. e i  = Y i  -  Y i ’ . Represented as vertical  distances along the Y axis.
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