In Keras, when you want to design a neural network where the last layer has a single output neuron (i.e., a single variable), you typically set up your model with a single neuron in the output layer, and you use an appropriate activation function based on the nature of your problem (e.g., linear for regression, sigmoid for binary classification, softmax for multiclass classification).

Here’s a detailed example of how to design a neural network with a single variable output at the last layer using Keras:

### Import Necessary Libraries:

from tensorflow import keras
from tensorflow.keras import layers

### Define Your Model:

Assuming a simple feedforward neural network, define your model using the Sequential API in Keras.

model = keras.Sequential()
# Add input layer and hidden layers
model.add(layers.Dense(units=64, activation='relu', input_shape=(input_size,)))
model.add(layers.Dense(units=32, activation='relu'))
# Add output layer with a single neuron (for a single variable output)
model.add(layers.Dense(units=1, activation='linear')) # Use 'linear' for regression tasks

Replace `input_size`

with the number of features in your input data.

### Compile the Model:

Compile the model by specifying the optimizer, loss function, and any additional metrics you want to track.

model.compile(optimizer='adam', loss='mean_squared_error') # Adjust the loss function based on your task

### Train the Model:

Assuming you have your training data (`X_train`

, `y_train`

), train the model.

model.fit(X_train, y_train, epochs=10, batch_size=32, validation_split=0.2) # Adjust parameters as needed

### Make Predictions:

Once trained, you can use the model to make predictions.

predictions = model.predict(X_test)

### Summary:

This is a basic example, and you might need to adjust the architecture, hyperparameters, and activation functions based on your specific problem (e.g., regression, binary classification, multiclass classification). The key point is to have a single neuron in the output layer and choose an appropriate activation function based on the task you are solving. If it’s a regression task, using a linear activation function is common. For classification tasks, choose an activation function like sigmoid or softmax based on the number of classes.