1. S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 14: 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

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

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

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

6. Example high school GPAFirst-year college GPA 3.53.3 2.52.2 43.5 3.82.7 2.83.5 1.92 3.23.1 3.73.4 2.71.9 3.33.7 Regression line, line of best fit Y’ = bX + a

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

8. Excel Y’ = bX + a b = SLOPE() a = INTERCEPT() high school GPAFirst-year college GPA 3.53.3 2.52.2 43.5 3.82.7 2.83.5 1.92 3.23.1 3.73.4 2.71.9 3.33.7 Slope (b)0.703893443 intercept (a)0.71977459 actual valuepredicted value 3.253.007428279

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.

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

11. Example BoxerReach(X)Win-p(Y) A6840 B8085 C7664 D8294 E6530

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

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

14. Standard Error of Estimate