42  Module 9 Cheat Sheet

Key concepts, definitions, and code from Chapters 21–22

A quick-reference summary of the essential ideas from Module 9. Click any section heading to jump to the full coverage in the book.

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Correlation

Correlation measures the strength and direction of a linear relationship between two numeric variables. It ranges from −1 (perfect negative) through 0 (none) to +1 (perfect positive).

import pandas as pd
import seaborn as sns

df['col_a'].corr(df['col_b'])   # a single pair
df.corr(numeric_only=True)       # full correlation matrix

sns.heatmap(df.corr(numeric_only=True), annot=True, cmap='coolwarm', center=0)
sns.scatterplot(data=df, x='col_a', y='col_b')   # always look before trusting r

	r
0.0 – 0.3	Weak
0.3 – 0.7	Moderate
0.7 – 1.0	Strong

Correlation only detects linear relationships and says nothing about causation. A strong curve can produce r ≈ 0, and a strong r can come from a lurking third variable. Plot the data.

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Linear Regression

Linear regression fits a straight line that predicts a continuous target from one or more features by minimizing the sum of squared errors.

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split

X = df[['feature_1', 'feature_2']]
y = df['target']

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=123
)

model = LinearRegression()
model.fit(X_train, y_train)

preds = model.predict(X_test)

model.intercept_    # the constant term
model.coef_         # one coefficient per feature, in column order

Reading coefficients: each coefficient is the expected change in the target for a one-unit increase in that feature, holding the other features constant.

# Pair coefficients with names so they are readable
pd.Series(model.coef_, index=X.columns).sort_values(ascending=False)

Categorical predictors must be converted to numeric columns first:

X = pd.get_dummies(df[['numeric_col', 'category_col']], drop_first=True)

drop_first=True avoids perfect collinearity — each dummy is then read relative to the omitted baseline category.

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Evaluating Regression Models

Regression finds the line minimizing SSE (sum of squared errors). SSE itself is not interpretable because it grows with dataset size and squared units, so we report derived metrics instead.

from sklearn.metrics import (
    r2_score,
    mean_squared_error,
    root_mean_squared_error,
    mean_absolute_error,
    mean_absolute_percentage_error,
)

r2   = r2_score(y_test, preds)
mse  = mean_squared_error(y_test, preds)
rmse = root_mean_squared_error(y_test, preds)   # sklearn >= 1.4
mae  = mean_absolute_error(y_test, preds)
mape = mean_absolute_percentage_error(y_test, preds)

Metric	Units	Reads as	Sensitive to outliers
R²	none (0–1)	Share of variance explained	Moderately
MSE	target²	Average squared error	Very
RMSE	target	Typical error, same units as target	Very
MAE	target	Average absolute error	Less
MAPE	percent	Average error as a % of actual	Breaks near zero

Choosing a metric:

Situation	Prefer
Large errors are disproportionately costly	RMSE
All errors cost about the same per unit	MAE
Stakeholders think in percentages	MAPE
Explaining overall fit to a non-technical audience	R²

Report metrics on the test set. Training metrics only tell you how well the model memorized. A large train/test gap is the signature of overfitting.

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Common Pitfalls

Mistake	Fix
Reading correlation as causation	Correlation constrains explanations; it does not establish them
Trusting r without plotting	Anscombe’s quartet: identical r, wildly different data
Comparing coefficients on different scales	Standardize features first, or compare within a single unit
Using MAPE when actuals near zero	Percent error explodes; use MAE instead
Reporting R² from the training set	Always evaluate on held-out data
Forgetting drop_first=True on dummies	Perfect collinearity makes coefficients unstable