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

2. Last week

3. This week
how prediction works 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

4. 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

5. 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

6. Example Regression line, line of best fit Y’ = bX + a high school GPA
First-year college GPA
3.5
3.3
2.5
2.2 4
3.8
2.7
2.8
1.9 2
3.2
3.1
3.7
3.4
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 GPA
First-year college GPA
3.5
3.3
2.5
2.2 4
3.8
2.7
2.8
1.9 2
3.2
3.1
3.7
3.4
Slope (b)
intercept (a)
actual value
predicted value
3.25

9. How good is our predication
Error of estimate
Standard error of estimate
The difference between the predicated Y and real Y

10. Exercise
S-p286 1 2 3 4