LINEAR REGRESSION

Follows a trend…

It is everywhere… You just have to look for it

What is Linear Regression -

When we see a relationship in a scatterplot, we can use a line to summarize the relationship in the data. We can also use that line to make predictions in the data. This process is called linear regression.

The General Formula -

It will always have an input, once equated, will give us the output -

f(x) = mx + c or y = mx + c

Where ;

m = slope or the gradient, shows the rate of change, common difference between the 2 consecutive points will be the value of 'm'.

∴

x = The input

c = Y - Intercept ; occurs when, x = 0

To find the equation of the line from the graph -

Step 1 - Find the slope.

This line goes through (0,40), (10,35) so the slope is m = (35 - 40) / (10 - 0)

∴ m = -1/2

A negative gradient means that the correlation between the y and x is negative, meaning, as the value of x increases, the value of y decreases.

Step 2 - Find the y-intercept.

We can see that the line passes through (0 , 40)

∴ c = 40

Step 3 - Write the equation in ' y = mx + c ' form.

∴ The equation is f(x) = -0.5x + 40