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
2 21 65 1365 441 4225
3 25 79 1975 625 6241
4 42 75 3150 1764 5625
5 57 87 4959 3249 7569
6 59 81 4779 3481 6561
Σ 247 486 20485 11409 40022
From the above table, Σx = 247, Σy = 486, Σxy = 20485, Σx2 = 11409, Σy2 = 40022. n is the sample size (6, in our case).
Step 2: Use the following equations to find a and b.
find a linear regression equation
a = 65.1416
b = .385225
Click here if you want easy, step-by-step instructions for solving this formula.
Find a:
((486 × 11,409) – ((247 × 20,485)) / 6 (11,409) – 2472)
484979 / 7445
=65.14
Find b:
(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.