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#### Minhanh

Hi everyone,

I am doing an optimization experiments with 3 factors at 3 levels of each variables, and I used Box-Benken design to design my experimental works. Total 15 runs was done and unfortunately, I do not know how to fit my data to the second-order popolynomial equation.

I did some preliminary analysis by Minitab 16, however I get so confusing that the model is fit or not best fit may data based on R-square, adjusted R-square and Lack of fit.

Staff member

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#### Minhanh

Thanks so much for your kind helps.

I would like to attach a Minitab project file for you have a look.

I did this experiment with expectation to observe how 3 factors effect to my measurements and their interactions if any. In addition, I would like to fit my data to a full quadratic model. It seems like that my data does not fit well. So if does not fit, should I plot contour/surface plot and do optimization? Please give me advice for this.

Thank you very much

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#### Miner

##### Forum Moderator
Staff member
I reviewed your experiment. The reason that you are unable to fit a model is that none of the model terms are statistically significant. The pure error term is very large compared to the factors. This is evidenced by the high p-values and low R^2(adj) and R^2(pred) even after simplifying the model.

There are a number of possibilities for this:
1. The levels selected for each factor might not be sufficient. While I do not know the units used for each factor the relative magnitude of the number seem to make this possibility unlikely.
2. The measurement system used to evaluate the response is inadequate. That is the measurement variation swamps any potential effect.
3. The factors have no effect on the response.

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#### Minhanh

Hi Miner,

Thank so much for taking your time and patient to explain to me my data analysis. Much appreciate your kindness

I still have little thing to wonder. Please help me get understand on it. As you explained, when we fit data to a model, we should consider to Lack of fit, R-square and adjusted R-square.

1. If R-square and adjusted R-square values are close together and exceed 90%, the model is adequate?

2. If only R-square is over 90% but adjusted-R square is small, the model is adequate to explain the response?

3. Is it right that if Lack of fit is bigger than 5%, the data is statistically significant? What is main meaning of Lack-of-fit value?

Thank you very much for many helps.

#### Miner

##### Forum Moderator
Staff member
1. If R-square and adjusted R-square values are close together and exceed 90%, the model is adequate?
This would typically be considered very good. However, much depends upon the use to which you intend to put the model. If you only need relationships and identification of significant factors values much lower would be adequate. Approximate predictions may be made with values above 70%. If you need precise predictions, values above 85% are recommended. These are only general guidelines. The final determinant is whether the model will suit your needs.
2. If only R-square is over 90% but adjusted-R square is small, the model is adequate to explain the response?
No. This is an indication that the model has been overfitted. That is, you have too many terms in the model that are either not significant, or add little value.

3. Is it right that if Lack of fit is bigger than 5%, the data is statistically significant? What is main meaning of Lack-of-fit value?
No. Lack of fit is an indication that you have insufficient terms in your model. For example, if you have a linear model, but your data is a quadratic curve, your lack of fit test will show significance until you add a quadratic term to your model.

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#### Minhanh

Hi Miner,

Heaps of thanks to your helps.

I get more understanding on statistical aspects. Thanks to Elsmar Cove Forum

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