# Documentation

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Class: LinearModel

Add terms to linear regression model

## Description

mdl1 = addTerms(mdl,terms) returns a linear model mdl1 that is the same as the input model mdl, but with additional terms as specified by terms.

## Input Arguments

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Full, fitted linear regression model, specified as a LinearModel object constructed using fitlm or stepwiselm.

Terms to add to the regression model mdl, specified as one of the following:

• Formula representing one or more terms to add. For details, see Wilkinson Notation.

• Row or rows in the terms matrix (see the modelspec argument description in the fitting function fitlm). For example, if there are three variables A, B, and C:

[0 0 0] represents a constant term or intercept
[0 1 0] represents B; equivalently, A^0 * B^1 * C^0
[1 0 1] represents A*C
[2 0 0] represents A^2
[0 1 2] represents B*(C^2)

## Output Arguments

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Regression model with additional terms, returned as a LinearModel object. mdl1 is the same as mdl but includes the additional terms specified in terms. To overwrite mdl, set mdl1 equal to mdl.

## Examples

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Create a model of the carsmall data without any interactions, then add an interaction term.

Load the carsmall data and make a model of the MPG as a function of weight and model year.

tbl = table(MPG,Weight);
tbl.Year = categorical(Model_Year);
mdl = fitlm(tbl,'MPG ~ Year + Weight^2');

Add an interaction term to mdl.

terms = 'Year*Weight';
mdl1 =

Linear regression model:
MPG ~ 1 + Weight*Year + Weight^2

Estimated Coefficients:
Estimate          SE         tStat        pValue
___________    __________    ________    __________

(Intercept)            48.045         6.779      7.0874    3.3967e-10
Weight              -0.012624     0.0041455     -3.0454     0.0030751
Year_76                2.7768        3.0538     0.90931        0.3657
Year_82                16.416        4.9802      3.2962     0.0014196
Weight:Year_76    -0.00020693    0.00092403    -0.22394       0.82333
Weight:Year_82     -0.0032574     0.0018919     -1.7217      0.088673
Weight^2           1.0121e-06      6.12e-07      1.6538       0.10177

Number of observations: 94, Error degrees of freedom: 87
Root Mean Squared Error: 2.76
F-statistic vs. constant model: 117, p-value = 1.88e-39

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## Alternatives

Use stepwiselm to select a model from a starting model, continuing until no single step is beneficial.

Use removeTerms to remove particular terms.

Use step to optimally improve the model by adding or removing terms.

## References

[1] Wilkinson, G. N., and C. E. Rogers. Symbolic description of factorial models for analysis of variance. J. Royal Statistics Society 22, pp. 392–399, 1973.