What is linear regression?

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Supervised and Unsupervised Learning are two primary types of machine learning, differing mainly in how they process and learn from data.

Linear regression is a fundamental statistical method used to model the relationship between a dependent variable and one or more independent variables. It’s commonly used for prediction and to understand how changes in input variables are associated with changes in the output.

Types of Linear Regression:

1. Simple Linear Regression:

   • Involves one independent variable.

   • The relationship is modeled with a straight line:

     $$y = mx + b$$

     Where:

     • $y$ is the dependent variable,

     • $x$ is the independent variable,

     • $m$ is the slope (how much $y$ changes with $x$),

     • $b$ is the y-intercept (value of $y$ when $x = 0$).

2. Multiple Linear Regression:

   • Involves two or more independent variables.

   • The model becomes:

     $$y = b_0 + b_1x_1 + b_2x_2 + \dots + b_nx_n$$

     Where each $b$ is a coefficient representing the contribution of each independent variable $x$ to the prediction of $y$.

Key Assumptions:

• Linearity: The relationship between variables is linear.

• Independence: Observations are independent of each other.

• Homoscedasticity: Constant variance of the errors.

• Normality of residuals: The error terms (residuals) are normally distributed.

Uses:

• Forecasting sales based on advertising spend.

• Estimating house prices based on features like size, location, and number of rooms.

• Analyzing trends in finance, healthcare, and social sciences.

In summary, linear regression is a simple yet powerful tool for understanding and predicting numerical outcomes based on input data.

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