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# 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 (pred)

...

...

...

...

T

## Analysis of variance

Source

DF

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