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anova

Class: LinearModel

Analysis of variance for linear model

Syntax

tbl = anova(mdl)
tbl = anova(mdl,anovatype)
tbl = anova(mdl,anovatype,sstype)

Description

tbl = anova(mdl) returns a table with summary ANOVA statistics.

tbl = anova(mdl,anovatype) returns ANOVA statistics of the chosen type.

tbl = anova(mdl,anovatype,sstype) computes ANOVA statistics using the chosen type of sum of squares.

Input Arguments

mdl

Linear model, as constructed by fitlm or stepwiselm.

anovatype

ANOVA type:

  • 'component'tbl displays a ‘components' ANOVA table, with sums of squares and F tests attributable to each term in the model except the constant term.

  • 'summary'tbl displays a summary ANOVA table with an F test for the model as a whole.

    • If there are both linear and higher-order terms, there is also an F test for the higher-order terms as a group.

    • If there are replications (multiple observations sharing the same predictor values), there is also an F test for lack-of-fit computed by decomposing the residual sum of squares into a sum of squares for the replicated observations and the remaining sum of squares.

Default: 'component'

sstype

When anovatype is 'component', choose the sum of squares type:

  • 1

  • 2

  • 3

  • 'h'

For details, see Sum of Squares.

Default: 'h'

Output Arguments

tbl

Table containing summary ANOVA statistics. tbl depends on anovatype:

  • 'component':

    • Sum of squares

    • Degrees of freedom

    • Mean squares

    • F statistic

    • p-value

    • Formula used for model

  • 'summary':

    • Total Sum of Squares

    • Model Sum of Squares

      • Linear Sum of Squares (present if model has powers or interactions)

      • Nonlinear Sum of Squares (present if model has powers or interactions)

    • Residual Sum of Squares

      • Lack-of-fit Sum of Squares (present if model has replicates)

      • Pure error Sum of Squares (present if model has replicates)

Examples

expand all

Component ANOVA Table

Create a component ANOVA table from a model of the carsmall data.

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

load carsmall
cars = table(MPG,Weight);
cars.Year = ordinal(Model_Year);
mdl = fitlm(cars,'MPG ~ Year + Weight^2');

Create an ANOVA table.

tbl = anova(mdl)
tbl = 

                SumSq     DF    MeanSq      F         pValue  
                ______    __    ______    ______    __________

    Weight      2050.2     1    2050.2    265.11    1.9885e-28
    Year        849.55     2    424.77    54.927    2.9042e-16
    Weight^2    76.688     1    76.688    9.9164     0.0022303
    Error       688.27    89    7.7334                        
  

Summary ANOVA Table

Create a summary ANOVA table from a model of the carsmall data.

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

load carsmall
cars = table(MPG,Weight);
cars.Year = ordinal(Model_Year);
mdl = fitlm(cars,'MPG ~ Year + Weight^2');

Create a summary ANOVA table.

tbl = anova(mdl,'summary')
tbl = 

                     SumSq     DF    MeanSq      F   
                     ______    __    ______    ______

    Total            6005.3    93    64.573          
    Model              5317     4    1329.3    171.88
    . Linear         5240.3     3    1746.8    225.87
    . Nonlinear      76.688     1    76.688    9.9164
    Residual         688.27    89    7.7334          
    . Lack of fit    663.77    86    7.7183    0.9451
    . Pure error       24.5     3    8.1667          


                       pValue  
                     __________

    Total                      
    Model            5.5208e-41
    . Linear         1.7302e-41
    . Nonlinear       0.0022303
    Residual                   
    . Lack of fit       0.62874
    . Pure error               

The summary ANOVA table shows tests for groups of terms. The nonlinear group consists of just the Weight^2 term, so it has the same p-value as that term in Component ANOVA Table. The F statistic comparing the residual sum of squares to a "pure error" estimate from replicated observations shows no evidence of lack of fit.

Alternatives

More complete ANOVA statistics are available in the anova1, anova2, and anovan functions.

See Also

How To

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