What is a plot?

• A visual representation of the data

Which data? How is it usually structured?

• In a table. For example:

import seaborn as sns

df = sns.load_dataset('mpg', index_col='name')
df.head()

How can you Visualice this DataFrame?

• We could make a point for every car based on
  1. weight
  2. mpg

sns.scatterplot(x='weight', y='mpg', data=df);

Which conclusions can you make out of this plot?

• Well, you may observe that the location of the points are descending as we move to the right

• This means that the weight of the car may produce a lower capacity to make kilometres mpg

How can you measure this relationship?

• Linear Regression

from sklearn.linear_model import LinearRegression

model = LinearRegression()
model.fit(X=df[['weight']], y=df.mpg)
model.__dict__

• Resulting in ↓

{'fit_intercept': True,
 'normalize': False,
 'copy_X': True,
 'n_jobs': None,
 'n_features_in_': 1,
 'coef_': array([-0.00767661]),
 '_residues': 7474.8140143821,
 'rank_': 1,
 'singular_': array([16873.20281508]),
 'intercept_': 46.31736442026565}

Which is the mathematical formula for this relationship?

$$mpg = 46.31 - 0.00767 \cdot weight$$

• This equation means that the mpg gets 0.00767 units lower for every unit that weight increases.

Could you visualise this equation in a plot?

• Absolutely, we could make the predictions from the original data and plot them.

Predictions

y_pred = model.predict(X=df[['weight']])

dfsel = df[['weight', 'mpg']].copy()
dfsel['prediction'] = y_pred

dfsel.head()

• Out of this table, you could observe that predictions don't exactly match the reality, but it approximates.

• For example, Ford Torino's mpg is 17.0, but our model predicts 19.84.

Model Visualization

sns.scatterplot(x='weight', y='mpg', data=dfsel)
sns.scatterplot(x='weight', y='prediction', data=dfsel);

1. The blue points represent the actual data.
2. The orange points represent the predictions of the model.

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