Linear Regression

Definition

DEF

Linear regression is a supervised regression algorithm that models the relationship between input features and a continuous output as a straight line (or hyperplane), by finding the weights that best fit the data.

Diagram

Calculation

Sample dataset

Age (x)	Weight (y)
24	62
25	63
21	72
27	62

• ‘x’ is the independent variable or input & ‘y’ is the dependent variable or the output or target
• ‘y’ is a linear function of ‘x’ (since ‘y’ depends on ‘x’)

Equation

Formula for best fit line in linear regression: $y=mx+c$

$or$ $y={\beta }_0+{\beta }_{1}x$ $or$ $h_{\theta }(x)={\theta }_0+{\theta }_{1}x$ where,

• ${\theta }_0$ = Intercept (i.e. when $x=0$, $h_{\theta }(x)={\theta }_0$, aka the point where you are meeting the y axis)
• ${\theta }_1$ = Slope or Coefficient (i.e. with 1 unit measurement in x-axis, what is the unit measurement in y-axis)

Aim

Main aim of a linear regression is to find out the best fit line, in such a way that the distance between the data points and the predicted points should the very less.

Hypothesis $h_{\theta }(x)={\theta }_0+{\theta }_{1}x$ i.e. predicted weight = intercept + slope × datapoint(Age)

Now, this formula is for just one point, but if we want to find out the entire line, we need to keep on changing ${\theta }_0$ and ${\theta }_1$. To find the new ${\theta }_0$ and ${\theta }_1$, we have to use the Cost Function.