# W3H - What Why When How  # ML: Simple Math

## My understanding of the math behind ML explained in the simplest possible way.

Simply put, Machine Learning is about training a machine (model) to predict output for a given input.

Let us try to understand the math behind the prediction part.

Can you predict a missing number in the pattern below?

``````(1, 10)
(2, 20)
(3, 30)
(4, 40)
(5, ?)
``````

That was quite simple. Try another one...

``````(0, 5)
(2, 3)
(6, -1)
(4, ?)
``````

This one isn't that obvious. But there's a simple way. Let us treat these as `(x,y)` co-ordinates and try to plot a graph. Now, were you able to find the missing number? Yes, it is 1 (the red dot).

Can we do it without a graph? The answer is a linear equation.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named a 'linear' equation.

The linear equation is given as -

y = mx + b

where,

m = slope (know more)

b = y-intercept (the point at which the line intersects the Y-axis) (know more)

Now, to find the value of `y` using the linear equation, for a given `x` we will need values of the slope `m` and the y-intercept `b`.

Consider the given points.

``````(x, y)
(0, 5)
(2, 3)
(6, -1)
``````

Fortunately, we have a point with `x = 0` so finding `b`, the y-intercept is easy.

Using the first point `(x, y) = (0, 5)` :

``````y = m * x + b
5 = m * 0 + b
5 = 0 + b
5 = b
``````

we got `b = 5`.

Using `b` as 5 and the second point in the table `(x, y) = (2, 3)`, let us find `m`, the slope.

``````y = m * x + b
3 = m * 2 + 5
3 - 5 = m * 2
-2 = m * 2
-2 / 2 = m
-1 = m
``````

we got `m = -1`.

Let us use `m = -1` and `b = 5` to find the missing number.

``````(x, y)
(4, ?)

y = m * x + b
y = -1 * 4 + 5
y = -4 + 5
y = 1
``````

We were finally able to find the missing number, 1.

In the next one, ML: Simple Model, we'll try to train a model to predict the value for the same example above.