Analyze Variability

Table of fits and residuals

  

Minitab displays a table of fits and residuals. Minitab calculates fitted values for all combinations of factor levels. You can use this table to:

·    Compare the observed natural log of the standard deviation to the fitted value to see which combinations of factor settings are better explained by the model.

·    Identify unusual observations in the data, which are identified by an X if the predictor is unusual (i.e., the leverage is greater than 3p/n or .99, whichever is smaller) or an R if the response is unusual (i.e., the absolute value of standardized residual is greater than 2).

Example Output

 
 

Fits and Diagnostics for All Observations

 

Original Response

 

                        Ratio

Obs     Std     Fit  Residual

  1  1.4131  1.5985    0.8840

  2  1.5567  1.3607    1.1440

  3  4.5696  4.2442    1.0767

  4  0.4565  0.4971    0.9184

  5  1.6529  1.5064    1.0973

  6  1.6812  1.8656    0.9011

  7  3.2686  3.4137    0.9575

  8  0.6144  0.5817    1.0562

  9  1.4041  1.5235    0.9216

 10  1.4070  1.3115    1.0729

 11  3.8516  3.3787    1.1400

 12  0.3550  0.4002    0.8872

 13  1.6272  1.4547    1.1186

 14  1.6472  1.8219    0.9041

 15  2.3432  2.7537    0.8509

 16  0.5514  0.4745    1.1620

 

 

Transformed Response

 

                                        Std

Obs  Ln(Std)  Ln(Fit)  Ln(Resid)  Ln(Resid)

  1    0.346    0.469     -0.123      -1.15

  2    0.443    0.308      0.135       1.25

  3    1.519    1.446      0.074       0.69

  4   -0.784   -0.699     -0.085      -0.79

  5    0.503    0.410      0.093       0.86

  6    0.520    0.624     -0.104      -0.97

  7    1.184    1.228     -0.043      -0.40

  8   -0.487   -0.542      0.055       0.51

  9    0.339    0.421     -0.082      -0.76

 10    0.341    0.271      0.070       0.65

 11    1.348    1.217      0.131       1.22

 12   -1.036   -0.916     -0.120      -1.11

 13    0.487    0.375      0.112       1.04

 14    0.499    0.600     -0.101      -0.94

 15    0.851    1.013     -0.161      -1.50

 16   -0.595   -0.746      0.150       1.40

Interpretation

In this example, the first row in the worksheet is the factors set at their low levels. For this observation, the natural log of the standard deviation of strength is 0.346 and the fitted value calculated from the regression coefficients is 0.469. All of the standardized residuals for the natural log of the standard deviation are between -2 and 2, so no unusual observations exist in the data.