Chapter 12: Association Between I-R Variables & Linear Regression (Part 2)

Regression Analysis: Regression Line

• Equation of the regression line: Y = a + bX
  • Y = Predicted score on the dependent variable.
  • X = Score on the independent variable.
  • a = Y-intercept (constant). It is the point where the regression line crosses the Y-axis (when X = 0).
  • b = Slope of the regression line (coefficient or parameter estimate). It indicates the unit change in Y for each unit change in X.

Case Example

• A table is presented with sample data, including values for X, Y, X - \bar{X}, (X - \bar{X})^2, Y - \bar{Y}, (Y - \bar{Y})^2, and (X - \bar{X})(Y - \bar{Y}).
• The means are calculated as: \bar{X} = 6 and \bar{Y} = 77.4

Regression Analysis: Method of Least Squares

• The regression line equation is Y = a + bX. Regression analysis minimizes prediction error using the