Probability and Statistics > Regression Analysis > Find a Regression slope intercept
Regression Slope Intercept: Overview
The regression slope intercept formula, b0 = y – b1 * x is really just an algebraic variation of the regression equation, y’ = b0 + b1x where “b0” is the y-intercept and b1x is the slope. Once you’ve found the linear regression equation, all that’s required is a little algebra to find the y-intercept (or the slope).
Note: You may also see the regression slope intercept formula written as a = y’ + bx. It’s the same formula with different variables: a is used for b0 and b is used for b1.
Regression Slope Intercept: Steps
Sample question: Find the regression slope intercept for the following set of data:
| 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 |
Step 1: Find the linear regression equation (you may have already been given it in the question). If you don’t know how, see: Find a linear regression equation. For this sample question, the linear regression equation is: y’ = 65.14 + .385225x
Step 2: Rearrange the linear regression equation using algebra to fit the regression slope intercept formula, b0 = y – b1 * x:
65.14 = y’ + .385225x
That’s the y-intercept!
Tip: You can also identify the slope from the formula, which is .385225.
Check out our Youtube channel for more tips and help. You’ll find video on how to find the linear regression equation by hand or using technology (like Excel).