Lesson 1: Simple Linear Regression

Simple Linear Regression

Regression is about finding the “best fit” line through a scatter of data points.

We assume a linear relationship between an independent variable ( $x$ ) and a dependent variable ( $y$ ).

$y = \beta_0 + \beta_1 x + \epsilon$

Imagine we are predicting House Price based on Size.

X ♠

The input variable.

(Square Feet)

X ♠

Feature

Y ♥

The output variable.

($$$)

Y ♥

Target

How do we find the “best” line? We minimize the sum of the squared differences (residuals) between the actual data points and the predicted line.

$\text{Minimize } \sum (y_i - \hat{y}_i)^2$

Fitting a line to data to make predictions.