1. Regression
    1. Want to draw the line through the scatterplot that minimizes the error in prediction
    2. Intuitively
    3. Least squares regression line - prediction line that minimizes S (Y-Y')2
  2. Constructing the Least Squares Regression Line: Regression of Y on X
    1. Remember line formula - Y = bX + a we want b and a to minimize the S (Y-Y')2
    2. By =
    3. Ay =
  3. Regression of X on Y
    1. Same equation does not work for X on Y
    2. Because
    3. So,
  4. The Standard Error of Estimate - average deviation of prediction errors about the regression line
    1. Like standard deviation
    2. floating mean
    3. sum prediction errors = 0, therefore must square
    4. must divide by N-2
    5. Then take square root
    6. Computational Formula:

      7.  

       

       

    7. Homoscedasticity - assumed variability of Y remains constant across all values of X
    8. Interpretation
      1. Larger SE means
      2. Standard Deviation and %ages
  5. Considerations
  6. Relationship of Regression and Correlation
    1. r = regression slope for standard scores
    2. Can derive BY and BX from r
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