Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Multiple linear regression

`b = regress(y,X)`

`[b,bint] = regress(y,X)`

`[b,bint,r] = regress(y,X)`

`[b,bint,r,rint] = regress(y,X)`

`[b,bint,r,rint,stats] = regress(y,X)`

`[___] = regress(y,X,alpha)`

`regress`

is useful when you simply need the output arguments of
the function and when you want to repeat fitting a model multiple times in a loop. If
you need to investigate a fitted regression model further, create a linear regression
model object `LinearModel`

by using `fitlm`

or `stepwiselm`

. A `LinearModel`

object provides more features than `regress`

.

Use the properties of

`LinearModel`

to investigate a fitted linear regression model. The object properties include information about coefficient estimates, summary statistics, fitting method, and input data.Use the object functions of

`LinearModel`

to predict responses and to modify, evaluate, and visualize the linear regression model.Unlike

`regress`

, the`fitlm`

function does not require a column of ones in the input data. A model created by`fitlm`

always includes an intercept term unless you specify not to include it by using the`'Intercept'`

name-value pair argument.You can find the information in the output of

`regress`

using the properties and object functions of`LinearModel`

.Output of `regress`

Equivalent Values in `LinearModel`

`b`

See the `Estimate`

column of the`Coefficients`

property.`bint`

Use the `coefCI`

function.`r`

See the `Raw`

column of the`Residuals`

property.`rint`

Not supported. Instead, use studentized residuals ( `Residuals`

property) and observation diagnostics (`Diagnostics`

property) to find outliers.`stats`

See the model display in the Command Window. You can find the statistics in the model properties ( `MSE`

and`Rsquared`

) and by using the`anova`

function.

[1] Chatterjee, S., and A. S. Hadi. “Influential Observations, High Leverage
Points, and Outliers in Linear Regression.” *Statistical
Science*. Vol. 1, 1986, pp. 379–416.

`LinearModel`

| `fitlm`

| `mvregress`

| `rcoplot`

| `stepwiselm`