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Simple Linear Regression

https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s

In general, there are 3 main stages in Linear regression:

1. Using Least-squares to fit a line to the data

2. Calculating

R^{2}

3. Calculating a

p-value

for

R^{2}

Using Least-squares to fit a line to the data

Takinf from https://www.youtube.com/watch?v=nk2CQITm_eo&t=267s

First, draw a line through the data.

Second, calculate the Residual sum of squares: Measure the distance from the line to each data point (residual), square each distance, and then add them up.

The distance from a line to a data point is called a residual

Then, we rotate the line a little bit and calculate the RSS. We do this many times.

...

Then, the line that represents the linear regression is the one corresponding to the rotation that has the least RSS. The regression equation:

$y=a+bx$

The equation is composed of 2 parameters:

Slope: $b$

The slope is the amount of change in units of $y$ for each unitchange in $x$ .

The $y-axis$ intercept: $a$