Linear regression

How to use my linear

you have to create a venv or install in global the requirements.txt

python3 -m venv [path]
source [path]/bin/activate
pip install -r requirements.txt

You have to train the model before predict

python ./training
it will plot the cost , plot repartition of the data, plot the data on the different scale
and print the  performance score of the model

After training you can predit prices of vehicule with x mileage

python ./predict
>[int mileage ]
> its print the result of the prediction

Linear regression is a statistic method use for modelisation between dependant variable and indepedant variable

In simple terms, it aims to establish a straight line that best fits the observed data points in a coordinate space.

How its work

Linear regression is based on this formula

> y^= theta0 + theta1 * x

To perform a linear regression we have to use a Gradient descent

Optimized algorithmn that learn by itself with a number of iterations and a learning rate It permit to find the minimum error of the linear regressions

The formula

t0 = learning * (1/ n_sample) * sum ( y^ - y)
t1 = learning * (1/ n_sample) * sum ( y^ - y) * mileages ( or x)

To calculate the error between predictions and real prices we can use few formula to see if the performance of the linear regression is good and if we dont have to change the lr , n_iterate

we can use

• R2 : 1 - (sum (prices - predict) ^ 2) / (sum (prices - mean_prices)^ 2)

it gave use a performance between [0;1]

• MSE ( mean square error) 1/n_samples - (prices​−predict ​) ^ 2
• its give us a value and our goal is to reduce the mse ( more the mse is near 0 the better is)

The importance of Normalisation or standardization

when we have different scale its crucial to normalize or standize our data , so the different scale can't ruin our model

Its permit to have our data on the same scale [0;1]

There two of transformation of the data

• We can use Z-scores ( standardization)

x - mean / std

• We can use min max (normalisation)
• (x- min_val) / ( max_val - min_val)

Dont forget to change the theta0 and theta1 if you use normalisation or standardization