How do i find a linear regression equation?

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.

SUBJECTAGE XGLUCOSE LEVEL YXYX2Y2
14399425718499801
2216513654414225
3257919756256241
44275315017645625
55787495932497569
65981477934816561
Σ247486204851140940022
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.