Lack of fit F test — ols_pure_error

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

Usage

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
rss: 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
df_rss: 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                             
#> ----------------------------------------------------------------------