# Calculate: Regression

November 5, 2008 by kltangen

Filed under How To Calculate, Regression

Think of regression as a 5-step process.

First, calculate the mean of X and the mean of Y.

Second, calculate the slope of the line (called b). To find the slope, divide the SSxy by the SS of the predictor. That is:

Third, calculate the Y intercept (called a). The formula is:

Fourth, make a prediction. Plug in your X. Since you’ve already calculated a and b, all you need is an X value and you can predict what Y will be. Use the formula for a straight line:

Fifth, estimate the accuracy of the prediction. Don’t worry, there’s a formula for that too. Here it is:

EXAMPLE

X Y

2 5

4 7

6 6

9 8

12 14

15 11

15 12

2 5

4 7

6 6

9 8

12 14

15 11

15 12

First, calculate the mean of X and the mean of Y. Each mean = 9.

Second, calculate the slope of the line (called b). To find the slope, divide the SSxy by the SS of the predictor. The SSx is 164; the SSy is 68; and the SSxy 92. So the slope (b) = .56.

Third, calculate the Y intercept (called a). So a = 9 – (.56 * 9) = 3.95.

Fourth, make a prediction. Use the formula for a straight line: Let’s assume that the X value is 8, we would predict that Y (which will call Y-prime so we know it’s a prediction) equals 8.44.

The standard deviation of Y is 3.12, and r = .87. So the standard error of estimate is 1.81. This means that we’re 68% sure that the real score will be 8.44, plus or minus 1.81. In other words, we’re fairly sure the score will be between 6.63 and 10.25.

NOW YOU CHOOSE:

Day 6: Regression

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Day 6: Regression

Bit More About Regression

Even More About Regression

Calculate Regression

Practice Problems

More Practice Problems

Word Problems

Sim1Sim2Sim3

Sim4Sim5Sim6

Sim7Sim8Sim9

Basic Facts About Regression

Vocabulary

Formulas

Quiz 6

Summary