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# Multilinear regression

Click on the Analyze button to open a window where you can choose the X and Y you wish to analyze. Select the result in column Y that you want to analyze. The number of repetitions (columns to be taken into account) should be entered. You may also enter the description of the result that you want to analyze (optional). In the example above the target result is 23 and at least equal to 20 but more than 25.
Launch the analysis by clicking Analyze. .

## Student- significance analysis

Interpretation involves taking advantage of the different analysis windows, in particular the analysis of factor significance through the use of the Student test. This menu shows the significance of the entirety of the factors (Column Signif) as well as their degree of significance (column Pro The weaker the Proba p the higher the probability that the factor will truly influence the result. A factor is considered significant if:
p < 0.05
If coefficients are non-significant (in red) then we can delete the model by clicking on "click" in the line to be deleted; The analysis will then restart. The list of "studyable" factors is in the left hand column. To add a factor, select the factor by checkin the "select" box.
A good method is to searc for the best model simply by looking for the one with first order effects. To do this, click on the button "best subsets" and enter the maximum number of X to be tested to get: Studies can also be carried out: descending and ascending order
Descending order studies are carried out by selecting all of the terms and then eliminating, at first, the factors where the VIF is very strong (VIF>10, VIF Variance Influence Factor) and then the factors that are less significant (those with a higher probability p) except for the constant. This analysis can be done automatically.
The model in our example is thus refined until we arrive at: The adjusted R ² gives us the percentage of observed variations in the experimental plan as explained in the model. In our example we get 93.3%, which is correct.
By validating the "quadratic terms" the quadratic terms among the analysis candidates are elminated or reset.
• Likewise with "interactive terms"
• Likewise with "cubic terms

This function allows Ellistat:
• To calculate the predicted result for a factor configuration:
• To find the degree of a factor to arrive at the given result. In order to calculate a predicted result, all that needs to be done is place the factor cursors on the retained degree, the theoretical result calculation will appear in the prediction box for the result.
To maximize or minimize the result just clikc on the corresponding buttons. Ellistat automatically generates the best configuration.
If we want to attain the result value by modifying a factor, enter the target value in the "target value" box and then choose the factor to be modified to attain the desired value. If it is not possible to attain the value in the variant range, Ellipse gives the best result possible by placing the factor at the extremes. The factor can then modified if desired.
To validate the result, Ellistat shows you the variant range of results possible from the prediction.
If you enter the obtained value during a validation test, Ellistat will calculate the prediction error based on the variant range.
Generally, prediction errors of less than 10% are admitted.

Pareto Gives the relative importance of factors in the variance analysis.

### Residuals For each line in the experimental plan, the table gives the result predicted by the plan as well as the difference between the prediction and the measuement (residual). If there is an elevated amount of residuals it will appear in orange or red.

### Residuals histogram

This diagram is especially useful when the number of residuals is higher than 15. It makes it possible to see if the distribution follows a normal normal distribution and to find the residual variance. ### Observed vs Predicted

This diagram makes it possible to clearly show if the model obtained is correct on the tests that have already been carried out. For this, a correlation between the value predicted by the model and the value measured during tests is carried out. In theory, the points must align on the y=x line traced in red. ### ANOVA

If several repetitions were carried out, then a variance analysis can be done on the mean result.
The analysis of this table is facilitated by the decision that appears in colour.
The grouping method can easily be applied to the factors by deleting and adding factors in the variance analysis. To do this, click on the YES/NO in the "Accepted" column on the line of the factor concerned.
Take care in the interpretation! The residual variance is calculated by taking into account the repetition variance in each line. If we make a Taguchi product plan the repetitions includ the variance of the Noise factor effect. The residual variance is considerably overestimated in this particular case and no factors are declared significant. The results of this ANAVAR should not be taken into account with Taguchi product plans.
If the residual sigma is known from another experiment than the experimental plan then the variance can be re-entered in order to carry out a variance analysis; This table shows the results of calculations of factor effects and interactions. The averages are found when each factor is at level 1 or level 2. The averages for each combination of retained interactions can also be found.

3D visualization makes better understanding how effects and interactions possible. Select 2 factors out of the whole and the graph will visually represent the result surface for these two factors. The image can be turned using the mouse ## A complete solution for Industry 4.0

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