Assess how much of the error in prediction is due to lack of model fit.

ols_pure_error_anova(model, ...)

## Arguments

model An object of class lm. Other parameters.

## Value

ols_pure_error_anova returns an object of class "ols_pure_error_anova". An object of class "ols_pure_error_anova" is a list containing the following components:

lackoffit

lack of fit sum of squares

pure_error

pure error sum of squares

regression sum of squares

ess

error sum of squares

total

total sum of squares

rms

regression mean square

ems

error mean square

lms

lack of fit mean square

pms

pure error mean square

rf

f statistic

lf

lack of fit f statistic

pr

p-value of f statistic

pl

p-value pf lack of fit f statistic

mpred

data.frame containing data for the response and predictor of the model

regression sum of squares degrees of freedom

df_ess

error sum of squares degrees of freedom

df_lof

lack of fit degrees of freedom

df_error

pure error degrees of freedom

final

data.frame; contains computed values used for the lack of fit f test

resp

character vector; name of response variable

preds

character vector; name of predictor variable

## Details

The residual sum of squares resulting from a regression can be decomposed into 2 components:

• Due to lack of fit

• Due to random variation

If most of the error is due to lack of fit and not just random error, the model should be discarded and a new model must be built.

## Note

The lack of fit F test works only with simple linear regression. Moreover, it is important that the data contains repeat observations i.e. replicates for at least one of the values of the predictor x. This test generally only applies to datasets with plenty of replicates.

## References

Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition). Chicago, IL., McGraw Hill/Irwin.

## Examples

model <- lm(mpg ~ disp, data = mtcars)
ols_pure_error_anova(model)#> Lack of Fit F Test
#> -----------------
#> Response :   mpg
#> Predictor:   disp
#>
#>                       Analysis of Variance Table
#> ----------------------------------------------------------------------
#>                 DF     Sum Sq     Mean Sq     F Value        Pr(>F)
#> ----------------------------------------------------------------------
#> disp             1    808.8885    808.8885    314.0095    1.934413e-17
#> Residual        30    317.1587    10.57196
#>  Lack of fit    25    304.2787    12.17115    4.724824      0.04563623
#>  Pure Error      5       12.88       2.576
#> ----------------------------------------------------------------------