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This tutorial will help you understand how Data Visualization can help to analyse patterns that may result in a Linear Regression model
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What is a plot?
Which data? How is it usually structured?
import seaborn as sns
df = sns.load_dataset('mpg', index_col='name')
df.head()
How can you Visualice this DataFrame?
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?
from sklearn.linear_model import LinearRegression
model = LinearRegression()
model.fit(X=df[['weight']], y=df.mpg)
model.__dict__
{'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?
$$mpg = 46.31 - 0.00767 \cdot weight$$
mpg gets 0.00767 units lower for every unit that weight increases.Could you visualise this equation in a plot?
y_pred = model.predict(X=df[['weight']])
dfsel = df[['weight', 'mpg']].copy()
dfsel['prediction'] = y_pred
dfsel.head()
| weight | mpg | prediction | |
|---|---|---|---|
| name | |||
| chevrolet chevelle malibu | 3504 | 18.0 | 19.418523 |
| buick skylark 320 | 3693 | 15.0 | 17.967643 |
| plymouth satellite | 3436 | 18.0 | 19.940532 |
| amc rebel sst | 3433 | 16.0 | 19.963562 |
| ford torino | 3449 | 17.0 | 19.840736 |
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.
sns.scatterplot(x='weight', y='mpg', data=dfsel)
sns.scatterplot(x='weight', y='prediction', data=dfsel);
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