How to Find a Linear Regression Equation: Overview
Regression analysis is used to find equations that fit data. Once we have the regression equation, we can use the model to make predictions. One type of regression analysis is linear analysis. When a correlation coefficient shows that data is likely to be able to predict future outcomes and a scatter plot of the data appears to form a straight line, you can use simple linear regression to find a predictive function. If you recall from elementary algebra, the equation for a line is y = mx + b. This article shows you how to take data, calculate linear regression, and find the equation y’ = a + bx. Note: If you’re taking AP statistics, you may see the equation written as b0 + b1x, which is the same thing (you’re just using the variables b0 + b1 instead of a + b.
Watch the video or read the steps below to find a linear regression equation by hand. Scroll to the bottom of the page if you would prefer to use Excel:
How to Find a Linear Regression Equation: Steps
Step 1: Make a chart of your data, filling in the columns in the same way as you would fill in the chart if you were finding the Pearson’s Correlation Coefficient.
|Subject||Age x||Glucose Level y||xy||x2||y2||1||43||99||4257||1849||9801|
From the above table, Σx = 247, Σy = 486, Σxy = 20485, Σx2 = 11409, Σy2 = 40022. n is the sample size (6, in our case).
a = 65.1416
b = .385225
- ((486 × 11,409) – ((247 × 20,485)) / 6 (11,409) – 2472)
- 484979 / 7445
- (6(20,485) – (247 × 486)) / (6 (11409) – 2472)
- (122,910 – 120,042) / 68,454 – 2472
- 2,868 / 7,445
- = .385225
Step 3: Insert the values into the equation.
y’ = a + bx
y’ = 65.14 + .385225x
That’s how to find a linear regression equation by hand!
Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!
* Note that this example has a low correlation coefficient, and therefore wouldn’t be too good at predicting anything.
Find a Linear Regression Equation in Excel
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