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## Fitting a Neural Network

Statistical Thinking for Industrial Problem Solving

In this video, we use the Chemical Manufacturing 2 data. We fit a neural network model for Yield using the options available in the standard version of JMP for this demo.

First, we select Analyze, then Predictive Modeling, and then Neural.

We start by adding Yield as the Y, Response variable.

For this video, we use only three variables for illustration: Vessel Size, Amine Supplier, and Carbamate Amount. We select these variables as X, Factor, and click OK.

For validation, we use a holdback portion. We’ll set the random seed to 1234 for reproducibility and use the default holdback portion of 0.333. That is, one third of the data will be held out of model building for validation.

In the standard version of JMP, you can fit a neural model with one hidden layer and the TanH activation function. The default model has three nodes in the hidden layer.

We’ll click Go to fit this model.

Let’s look at the diagram for this model. To do this, we select Diagram from the red triangle for the model. This model has three variables in the input layer, the one hidden layer with three nodes, and the output layer.

Statistics for the training and the holdout validation data are provided. For this model, the RMSE is 2.73 and the RSquare is 0.233.

Let’s look at the parameter estimates for this model. To display the estimates, we select Show Estimates from the red triangle for the model.

There are parameter estimates for the hidden layers and for the output layer.

For each node in the hidden layer, there is an intercept and parameter estimates for each of the input variables. There is one parameter estimate for the continuous predictor (Carbamate Amount), and one parameter estimate for the two-level categorical predictor (Amine Supplier). Vessel Size has three levels, so there are two parameter estimates.

To see how these estimates are used to predict Yield, we select Save Formulas from the red triangle for the model.

This saves columns for each node in the hidden layer, and also saves a column for the predicted Yield. When we look at the formula in one of the hidden layers, you can see that the TanH function was used.

Let’s look at the formula for Predicted Yield. You can see that this is simply a linear combination of the outputs from each node in the hidden layer.

To explore this model, we can use the prediction profiler. To do this, we select Profiler from the red triangle for the model.

You can see how the predicted yield changes as we change the values of the predictors.

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