Intreprating a Data Set with Minitab - Help wanted

[enjoyneer]

hi ...below some data is given please help me in interpreting......

no of cases analysed are 14.....

Regression Analysis: RI versus Fe(T), %FeO, ...

The regression equation is
RI = 350 - 3.91 Fe(T) - 2.18 %FeO - 4.63 %MgO - 307 %K2O - 172 %P
+ 4.24 Basicity - 0.910 MPS


Predictor Coef SE coef T P VIF
Constant 349.87 45.35 7.72 0.000
Fe(T) -3.9053 0.5386 -7.25 0.000 3.181
%FeO -2.1818 0.4434 -4.92 0.003 2.334
%MgO -4.626 1.791 -2.58 0.042 2.459
%K2O -306.91 49.69 -6.18 0.001 4.061
%P -172.18 67.17 -2.56 0.043 4.728
Basicity 4.240 3.127 1.36 0.224 4.300
MPS -0.9102 0.3350 -2.72 0.035 1.268


S = 0.802628 R-Sq = 97.5% R-Sq(adj) = 94.5%

PRESS = 17.8900 R-Sq(pred) = 88.30%


Analysis of Variance

Source DF SS MS F P
Regression 7 149.020 21.289 33.05 0.000
Residual Error 6 3.865 0.644
Total 13 152.886


There are no replicates.
Minitab cannot do the lack of fit test based on pure error.


Source DF Seq SS
Fe(T) 1 9.016
%FeO 1 30.366
%MgO 1 0.612
%K2O 1 71.800
%P 1 31.370
Basicity 1 1.100
MPS 1 4.756


Unusual Observations

Obs Fe(T) RI Fit SE Fit Residual St Resid
4 56.3 45.620 44.627 0.639 0.993 2.05R

R denotes an observation with a large standardized residual.





please also tell me the correct approach if you have any...........

 

[Barbara B]

enjoyneer,

could you please share the data with us, not only the results? It will be far more easier to evaluate your approach and/or to develop other ideas for the analysis.

Thanks in advance,

Barbara

 

[steelejc15425]

Hi Enjoyneer,

I think Barbara's right that we need more information about your data set. From the representation of your predictors, %FeO, %MgO, etc., it looks like you may have a restricted range of potential values that you could use for predicting values of your response. Rather than Regression, Minitab might provide better tools if we define a custom mixtures design for you to analyze your data with.

With that said, I think that the first things to look at in the output you provide is the unusual observation. If it is important to describe or predict the data at the values for the predictors from observation 4, then we should really be worried about using the model that's been calculated.

You should also use Minitab to produce residual plots that might reveal problems with the model. If you used Stat > Regression > Regression to produce this output, then you can make residual plots by clicking the Graphs button and turning on the 4-in-1 plot. Patterns, outliers, or a curved normal probability plot could mean that the model doesn't describe the data well.

I'm assuming that you're including all of the predictors in your data. If you want to predict new observations, you might want to consider some subsets of these variables to see if you can get close to or better fit statistics (R^2, Press, S, etc.).

I think it would also be worth looking at the magnitude of the coefficients while you do this. These are essentially slopes--if the predictor variable increases by 1, the coefficient is the change the model predicts in the response. The size of the %K2O coefficient compared to FeO and MgO makes me wonder if perhaps only some of your predictors are have practical considerations. However, this depends on whether the units of the predictors are comparable, which would be easier to consider if, as Barbara suggests, we had the chance to see your data.