Probability and Statistics > Regression Analysis > Find a Regression slope intercept

## Regression Slope Intercept: Overview

The regression slope intercept formula, b

_{0}= y – b

_{1}* x is really just an algebraic variation of the regression equation, y’ = b

_{0}+ b

_{1}x where “b

_{0}” is the y-intercept and b

_{1}x 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 b_{0} and b is used for b_{1}.

## Regression Slope Intercept: Steps

**Sample question: **Find the regression slope intercept for the following set of data:

Subject | Age x | Glucose Level y | xy | x^{2} |
y^{2} |
---|---|---|---|---|---|

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, b_{0} = y – b_{1} * 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).

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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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