# Minitab regression analysis

Minitab provides a regression analysis for a predictor variable and a response variable via,

Stat > Regression > Regression > Fit regression model

Minitab returns an analysis consisting of various tables,

## Regression equation

Minitab returns a regression equation in the conventional format,

## Coefficients table

Minitab's official documentation discusses interpretation here: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/regression/how-to/fit-regression-model/interpret-the-results/all-statistics-and-graphs/coefficients-table/

Term | Coef | SE Coef | T-Value | P-Value | VIF |
---|---|---|---|---|---|

Constant | Y-intercept point ( | ... | Y-intercept's t-statistic. | ... | ... |

Predictor | Slope of the line ( | ... | Slope's t-statistic. | ... | ... |

The constant is another term for the y-intercept. Moving the regression up or down (moving the y-intercept up or done) is crucial in ensuring that our residuals have a mean that is as close to zero as possible. The constant (a.k.a. "y-intercept) row is generally meaningless, but it does tell us about bias that may not be reflected elsewhere in our model (blog.minitab.com).

The slope's t-statistic tests our null hypothesis that the slope equals zero, or in other words, that there is no relation.

## Model summary

Minitab's official documentation discusses interpretation here: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/regression/how-to/fit-regression-model/interpret-the-results/all-statistics-and-graphs/model-summary-table/

S | R-sq | R-sq (adj) | R-sq (pred) |
---|---|---|---|

... | ... | ... | ... |

T

## Analysis of variance

Source | DF | Adj SS | Adj MS | F-Value | P-Value |
---|---|---|---|---|---|

Regression | 1 | ... | ... | ... | ... |

Predictor | 1 | ... | ... | ... | ... |

Error | n-2 | ... | ... | ||

Lack-of-Fit | c-2 | ... | ... | ... | ... |

Pure Error | n-c | ... | ... | ||

Total | n-1 | ... |

Where n = sample size, and c = unique observations.

More information is given here: Analysis of Variance (ANOVA) table and F-test

## Fits and Diagnostics for Unusual Observations

Obs | Response | Fit | Resid | Std Resid | |
---|---|---|---|---|---|

... | ... | ... | ... | ... | X or R |

... | ... | ... | ... | ... | X or R |

R = Large Residual

X = Unusual X