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Social Statistics: Linear regression

Social Statistics: Linear regression. This week. How to predict and how it can be used in the social and behavioral sciences How to judge the accuracy of predictions INTERCEPT and SLOPE functions Multiple regression. Prediction.

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Social Statistics: Linear regression

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  1. Social Statistics: Linear regression

  2. This week • How to predict and how it can be used in the social and behavioral sciences • How to judge the accuracy of predictions • INTERCEPT and SLOPE functions • Multiple regression S519

  3. Prediction • Based on the correlation, you can predict the value of one variable from the value of another. • Based on the previously collected data, calculate the correlation between these two variable, use that correlation and the value of X to predict Y • The higher the absolute value of the correlation coefficient, the more accurate the prediction is of one variable from the other based on that correlation S519

  4. Logic of prediction • Prediction is an activity that computes future outcomes from present ones. • When we want to predict one variable from another, we need to first compute the correlation between the two variables S519

  5. Type of regression • Linear regression • One independent variable • Multi-independent variables • Non-linear regression • Power • Exponential • Quadric • Cubic • etc S519

  6. Example Regression line, line of best fit Y’ = bX + a S519

  7. Regression line • Y’ = bX + a Y’ = 0.704X + 0.719 Y’ (read Y prime) is the predicted value of Y S519

  8. Excel • Y’ = bX + a • b = SLOPE() • a = INTERCEPT() S519

  9. How good is our predication • Error of estimate • Standard error of estimate • The difference between the predicated Y and real Y • Standard error of estimate is very similar to the standard deviation. S519

  10. Example • You are a talent scout looking for new boxers to train. For a group of 6 pro boxers, you record their reach (inches) and the percentage of wins (wins/total*100) over his career. Create a regression equation to predict the success of a boxer given his reach S519

  11. Example S519

  12. Example • Making predictions from our equation • What winning percentage would you predict for “T-rex Arms” Timmy, who has a reach of 62-inches • We would predict 18.44% of Timmy’s fights to be wins S519

  13. Example • Making predictions from our equation • What winning percentage would you predict for “Ape-Arms” Al, who has a reach of 84-inches? • We would predict 98.08% of Al’s fights to be wins S519

  14. Standard Error of Estimate S519

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