# removeTerms

Remove terms from linear regression model

## Syntax

``NewMdl = removeTerms(mdl,terms)``

## Description

example

````NewMdl = removeTerms(mdl,terms)` returns a linear regression model fitted using the input data and settings in `mdl` with the terms `terms` removed.```

## Examples

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Create a linear regression model using the `hald` data set. Remove terms that have high p-values.

```load hald X = ingredients; % predictor variables y = heat; % response variable```

Fit a linear regression model to the data.

`mdl = fitlm(X,y)`
```mdl = Linear regression model: y ~ 1 + x1 + x2 + x3 + x4 Estimated Coefficients: Estimate SE tStat pValue ________ _______ ________ ________ (Intercept) 62.405 70.071 0.8906 0.39913 x1 1.5511 0.74477 2.0827 0.070822 x2 0.51017 0.72379 0.70486 0.5009 x3 0.10191 0.75471 0.13503 0.89592 x4 -0.14406 0.70905 -0.20317 0.84407 Number of observations: 13, Error degrees of freedom: 8 Root Mean Squared Error: 2.45 R-squared: 0.982, Adjusted R-Squared: 0.974 F-statistic vs. constant model: 111, p-value = 4.76e-07 ```

Remove the `x3` and `x4` terms because their p-values are high.

```terms = 'x3 + x4'; % terms to remove NewMdl = removeTerms(mdl,terms)```
```NewMdl = Linear regression model: y ~ 1 + x1 + x2 Estimated Coefficients: Estimate SE tStat pValue ________ ________ ______ __________ (Intercept) 52.577 2.2862 22.998 5.4566e-10 x1 1.4683 0.1213 12.105 2.6922e-07 x2 0.66225 0.045855 14.442 5.029e-08 Number of observations: 13, Error degrees of freedom: 10 Root Mean Squared Error: 2.41 R-squared: 0.979, Adjusted R-Squared: 0.974 F-statistic vs. constant model: 230, p-value = 4.41e-09 ```

`NewMdl` has the same adjusted R-squared value (0.974) as the previous model, meaning the fit is as good in the new model. All the terms in the new model have extremely low p-values.

## Input Arguments

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Linear regression model, specified as a `LinearModel` object created using `fitlm` or `stepwiselm`.

Terms to remove from the regression model `mdl`, specified as one of the following:

• Character vector or string scalar formula in Wilkinson Notation representing one or more terms. The variable names in the formula must be valid MATLAB® identifiers.

• Terms matrix `T` of size t-by-p, where t is the number of terms and p is the number of predictor variables in `mdl`. The value of `T(i,j)` is the exponent of variable `j` in term `i`.

For example, suppose `mdl` has three variables `A`, `B`, and `C` in that order. Each row of `T` represents one term:

• `[0 0 0]` — Constant term or intercept

• `[0 1 0]``B`; equivalently, `A^0 * B^1 * C^0`

• `[1 0 1]``A*C`

• `[2 0 0]``A^2`

• `[0 1 2]``B*(C^2)`

`removeTerms` treats a group of indicator variables for a categorical predictor as a single variable. Therefore, you cannot specify an indicator variable to remove from the model. If you specify a categorical predictor to remove from the model, `removeTerms` removes a group of indicator variables for the predictor in one step. See Modify Linear Regression Model Using step for an example that describes how to create indicator variables manually and treat each one as a separate variable.

## Output Arguments

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Linear regression model with fewer terms, returned as a `LinearModel` object. `NewMdl` is a newly fitted model that uses the input data and settings in `mdl` with the terms specified in `terms` removed from `mdl`.

To overwrite the input argument `mdl`, assign the newly fitted model to `mdl`:

`mdl = removeTerms(mdl,terms);`

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### Wilkinson Notation

Wilkinson notation describes the terms present in a model. The notation relates to the terms present in a model, not to the multipliers (coefficients) of those terms.

Wilkinson notation uses these symbols:

• `+` means include the next variable.

• `–` means do not include the next variable.

• `:` defines an interaction, which is a product of terms.

• `*` defines an interaction and all lower-order terms.

• `^` raises the predictor to a power, exactly as in `*` repeated, so `^` includes lower-order terms as well.

• `()` groups terms.

This table shows typical examples of Wilkinson notation.

Wilkinson NotationTerms in Standard Notation
`1`Constant (intercept) term
`x1^k`, where `k` is a positive integer`x1`, `x12`, ..., `x1k`
`x1 + x2``x1`, `x2`
`x1*x2``x1`, `x2`, `x1*x2`
`x1:x2``x1*x2` only
`–x2`Do not include `x2`
`x1*x2 + x3``x1`, `x2`, `x3`, `x1*x2`
`x1 + x2 + x3 + x1:x2``x1`, `x2`, `x3`, `x1*x2`
`x1*x2*x3 – x1:x2:x3``x1`, `x2`, `x3`, `x1*x2`, `x1*x3`, `x2*x3`
`x1*(x2 + x3)``x1`, `x2`, `x3`, `x1*x2`, `x1*x3`

For more details, see Wilkinson Notation.

## Algorithms

• `removeTerms` treats a categorical predictor as follows:

• A model with a categorical predictor that has L levels (categories) includes L – 1 indicator variables. The model uses the first category as a reference level, so it does not include the indicator variable for the reference level. If the data type of the categorical predictor is `categorical`, then you can check the order of categories by using `categories` and reorder the categories by using `reordercats` to customize the reference level. For more details about creating indicator variables, see Automatic Creation of Dummy Variables.

• `removeTerms` treats the group of L – 1 indicator variables as a single variable. If you want to treat the indicator variables as distinct predictor variables, create indicator variables manually by using `dummyvar`. Then use the indicator variables, except the one corresponding to the reference level of the categorical variable, when you fit a model. For the categorical predictor `X`, if you specify all columns of `dummyvar(X)` and an intercept term as predictors, then the design matrix becomes rank deficient.

• Interaction terms between a continuous predictor and a categorical predictor with L levels consist of the element-wise product of the L – 1 indicator variables with the continuous predictor.

• Interaction terms between two categorical predictors with L and M levels consist of the (L – 1)*(M – 1) indicator variables to include all possible combinations of the two categorical predictor levels.

• You cannot specify higher-order terms for a categorical predictor because the square of an indicator is equal to itself.

## Extended Capabilities

Introduced in R2012a