S519: Evaluation of Information Systems

Social Statistics

Inferential Statistics

Chapter 14: 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

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

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

Type of regression

Linear regression One independent variable Multi-independent variables

Non-linear regression Power Exponential Quadric Cubic etc.

baxy bxaxaxay nn ...2211

cbxaxy 2

baxy xay

dcxbxaxy 23

Example

high school GPA First-year college GPA3.5 3.32.5 2.2

4 3.53.8 2.72.8 3.51.9 23.2 3.13.7 3.42.7 1.93.3 3.7

Regression line, line of best fit

Y’ = bX + a

Regression line

Y’ = bX + a

nXX

nYXXYb

/)(

)/(22

n

XbYa

Y’ = 0.704X + 0.719

Y’ (read Y prime) is the predicted value of Y

Excel

Y’ = bX + a b = SLOPE() a = INTERCEPT()

high school GPA First-year college GPA3.5 3.32.5 2.2

4 3.53.8 2.72.8 3.51.9 23.2 3.13.7 3.42.7 1.93.3 3.7

Slope (b) 0.703893443intercept (a) 0.71977459

actual value predicted value3.25 3.007428279

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.

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

Example

Boxer Reach(X)

Win-p(Y)

A 68 40

B 80 85

C 76 64

D 82 94

E 65 30

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

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

Standard Error of Estimate