Suppose we want to predict the outcome of a battle between two ancient Greek armies based on various factors, such as the size of the armies, the quality of their weapons, and the experience of their commanders. We can use linear regression to create a model that predicts the probability of each army winning the battle based on these factors.

``` import numpy as np from sklearn.linear<sub>model</sub> import LinearRegression

X = np.array([[100, 50, 3], [200, 100, 5], [300, 150, 7], [400, 200, 9]]) y = np.array([0, 0, 1, 1])

model = LinearRegression() model.fit(X, y)

X<sub>test</sub> = np.array([[150, 75, 4], [250, 125, 6]]) y<sub>pred</sub> = model.predict(X<sub>test</sub>)

print(y<sub>pred</sub>) # Expected output: [0.17, 0.52] ```

In this example, the training data represents four battles with known outcomes, and the features are the size of the armies, the quality of their weapons, and the experience of their commanders. The model is then trained to predict the outcome of a battle given these features, and it can be tested with new data.

Suppose we have a dataset of mythological creatures, such as centaurs, harpies, and minotaurs, and we want to create a model that can classify new creatures based on their features, such as their size, speed, and strength. We can use logistic regression to create a model that predicts the probability of each creature belonging to a certain class.

``` import numpy as np from sklearn.linear<sub>model</sub> import LogisticRegression

X = np.array([[10, 20, 30], [20, 30, 40], [30, 40, 50], [40, 50, 60], [50, 60, 70], [60, 70, 80]]) y = np.array(['centaur', 'harpy', 'minotaur', 'centaur', 'harpy', 'minotaur'])

model = LogisticRegression() model.fit(X, y)

X<sub>test</sub> = np.array([[15, 25, 35], [35, 45, 55], [55, 65, 75]]) y<sub>pred</sub> = model.predict(X<sub>test</sub>)

print(y<sub>pred</sub>) # Expected output: ['centaur', 'harpy', 'minotaur']

```

In this example, the training data represents six mythological creatures with known classes, and the features are their size, speed, and strength. The model is then trained to classify new creatures based on these features, and it can be tested with new data.

Suppose we have a dataset of prophecies that have either come true or not, and we want to create a model that can predict whether a new prophecy is likely to come true or not. However, the dataset is biased, as some prophecies have been recorded more frequently than others, and this may affect the accuracy of the model. We can use the confusion matrix to identify and quantify the bias.