The linear model

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So far we learn what training a dataset involves and establish that we will focus on supervised learning.

It is time for the second piece of the puzzle.

The model let’s consider a variable x the function f of x gives us an output y y is a function of x

but we don’t know this function.

We want to make the algorithm find out on its own.

This is done by providing it with many pairs of observations of x and y as possible and following the

methodology to come.

All right let’s start with the simplest model possible the linear model display appearing oversimplified.

It is extremely important as it is the basis for more complicated models including non-linear ones in

the linear model universe f of x is x times w Plus P x is the input we have in the traditional statistical

jargon we would call w the coefficient of x and B would be the intercept in machine learning though

W is called The Weight or weights when we have more than one parameter b is called the bias or biases.

There are many ways to define the linear model w times x x times w x transpose times w or W transpose

times x.

It doesn’t matter.

We will keep the linear model simple and represent it in the following way X times w plus B.

The goal of the machine learning algorithm would be to find such values for W and B.

So the output of X times w plus B is as close to the observed values as possible.

OK let’s see an example.

See our goal is to predict the price of an apartment.

We may do that based on its size.

So the input X is the size X times w plus B is the model we are using the calculation of this expression

gives us the price or the output y let’s input real values.

The size of an apartment is seven hundred forty three square feet.

A possible model for predicting its price is X times three hundred thirty six point one minus three

thousand two hundred thirty seven point five.

One the wait is three hundred thirty six point one and the bias is minus three thousand two hundred

thirty seven point five one.

If we calculate the output following this model for seven hundred forty three square feet apartment

we would obtain a price of two hundred forty six thousand four hundred eighty four dollars and seventy

nine cents.

Similarily given an apartment of a different size say 1000 square feet our model would predict a price

of three hundred thirty two thousand eight hundred sixty two dollars and forty nine cents.

Knowing the size of any apartment we can get a prediction of its price based on the linear model.

Note this example oversimplifies how things work in practice.

But don’t worry we will get there soon enough.

Thanks for watching.

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