Mathematical Intuition of Linear Regression

Question

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Linear Regression Line

The line is drawn between two axes, X and Y.

We can draw infinite lines with different points. But only one will be best fit for the given points.

For a set of 2D points (x_i,y_i), the simplest linear regression model is:

y = mx + b

Where:

• (m) = slope
• (b) = intercept

To compute them from your points:

Slope:

m = (n∑xy−(∑x)(∑y)) / (n∑x^2−(∑x)^2)

Intercept:

b = (∑y−m∑x) / n

Then your best-fit line is:

y = mx + b

Calculation of Slope

For example points:

x	y
1	2
2	3
3	5
4	4

Result:
m = 0.8
b = 1.5

Best-fit line:
y = 0.8x + 1.5

Finally we get the result:

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