Explain linear regression.

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Linear Regression is one of the simplest and most widely used algorithms in machine learning and statistics. It is a supervised learning method used for predicting a continuous numerical value based on the relationship between input features and an output variable.

🔹 Core Idea

Linear regression assumes that there is a linear relationship between input variable(s) (features) and the output variable (label).
Mathematically, the relationship is modeled as:

$$y = m x + b$$

• y → predicted output (label)

• x → input feature

• m → slope/weight (shows how strongly x affects y)

• b → intercept (value of y when x = 0)

For multiple features, it becomes:

$$y = w_1x_1 + w_2x_2 + \dots + w_nx_n + b$$

🔹 Example

Suppose we want to predict house prices:

• Features: Size of house, number of rooms, location score

• Label: Price of house
  Linear regression will learn a formula like:

$$Price = 2000 \times (Size) + 50,000 \times (Rooms) + 1,00,000 \times (Location) + 2,00,000$$

This allows predicting prices for new houses.

🔹 Training Linear Regression

• The algorithm fits a line (or hyperplane) to minimize the difference between predicted values and actual labels.

• This difference is measured using loss functions (commonly Mean Squared Error – MSE).

• Optimization methods like Gradient Descent adjust the weights until the best fit is found.

🔹 Types of Linear Regression

1. Simple Linear Regression → One feature, one label.

2. Multiple Linear Regression → Multiple features, one label.

🔹 Applications

• Predicting house or stock prices

• Estimating sales revenue based on marketing spend

• Forecasting demand or growth trends

• Risk assessment in finance

✅ In short:
Linear regression fits a straight line (or hyperplane) to data, showing how inputs (features) relate to outputs (labels), and is used for prediction of continuous values.

Read more :

What is the difference between training, validation, and test sets?

What are features and labels in ML?

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