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

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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

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

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

Regression line Y’ = bX + a 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 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) 0.703893443 intercept (a) 0.71977459 actual value predicted value 3.25 3.007428279

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

Exercise S-p286 1 2 3 4