Regression Analysis in Machine Learning

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Regression analysis is a statistical technique in machine learning used to predict continuous numeric values by exploring the relationship between independent (predictor) and dependent (target) variables. Its primary objective is to estimate how a change in one or more predictors affects the outcome variable and to plot a best-fitting line or curve that models the relationship.

Key Terminologies

Term	Description
Independent Variables	Input features (predictors) used to predict output.
Dependent Variable	The output value we want to predict (target).
Regression Line	A best-fit line or curve that describes the relationship.
Overfitting	Model fits training data too well but fails to generalize.
Underfitting	Model fails to capture underlying trend (too simplistic).
Outliers	Extreme data points deviating from other observations.
Multicollinearity	Predictors are correlated with each other, which can distort the model.

How Regression Works

• Use labeled data (with known inputs and outputs).

• Train a model to learn the relationship between features and the target.

• Use the model to predict continuous output for new input data.

Types of Regression Models in ML

Type	Description
Linear Regression	Predicts output using a straight line: Y = mX + b.
Logistic Regression	Used for classification; outputs probability (0 to 1).
Polynomial Regression	Fits data with a polynomial curve (non-linear).
Lasso Regression	L1 regularization; shrinks less important features.
Ridge Regression	L2 regularization; helps in multicollinearity.
Decision Tree Regression	Splits data into tree nodes to predict values.
Random Forest Regression	Ensemble of trees; improves accuracy, reduces variance.
Support Vector Regression (SVR)	Uses support vectors for linear/non-linear regression.

Regression Model Types

• Simple Regression: One independent variable.

• Multiple Regression: Multiple independent variables.

How to Choose the Best Regression Model

1. Compare performance metrics:

   • MAE, MSE, RMSE, R², MAPE

2. Check model complexity & interpretability.

3. Evaluate generalization on test data.

Evaluation Metrics

Metric	Description
MAE	Average absolute error.
MSE	Average squared error.
RMSE	Square root of MSE.
R² Score	Proportion of variance explained (1 is best).
MAPE	Error as a percentage of true values.
Median Absolute Error	Robust to outliers.

Building a Regressor in Python

You can build regression models using libraries like Scikit-learn, TensorFlow, and Statsmodels.

Example with Scikit-learn:

from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
import pandas as pd

# Load dataset
X = dataset[['feature1', 'feature2']]
y = dataset['target']

# Split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

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

# Predict
predictions = model.predict(X_test)

# Evaluate
mse = mean_squared_error(y_test, predictions)
print("MSE:", mse)

Keywords

regression analysis, machine learning, linear regression, logistic regression, polynomial regression, lasso regression, ridge regression, support vector regression, decision tree regression, random forest regression, overfitting, underfitting, multicollinearity, prediction, evaluation metrics, mean squared error, root mean squared error, R-squared, model selection, feature selection