# Linear regression internet adoption in Colombia

Linear regression is a statistic method useful to make predictions, in this post we will generate a linear regression over public data from Colombian Goverment about Internet growth.

## Tools to use

• Python : We will use it to format data.
• Octave : We will use it to generate regression data.

## Formating the data

Data from Colombian Goverment contains several variables about different topics, We need to process this data and generate a simple cvs file where first column Will be months since first measure (Oct 2011) and the second value will be the number of internet affiliates by period. The first step is to get raw data:

    http://estrategiaticolombia.co/estadisticas/opendata/dat_dedicado_general.json


Now We can use a simple python script to format the data to feed octave:


from decimal import *

import json
import csv

def total_by_period(jf):
"""
And generate total  by period
"""
i = 0
data_dict = {}

def proccess_record(line):
"""
Process every line inside file in order to get a consolidate
"""
period_key = '{}-{}'.format(j_line['ANHO'], j_line['PERIODO'])
j_line['SUSCRIPTORES'] = Decimal(j_line['SUSCRIPTORES'])
if period_key not in data_dict:
record = {
'total': j_line['SUSCRIPTORES']
}
data_dict[period_key]  = record

else:
val = j_line['SUSCRIPTORES']
data_dict[period_key]['total'] += val

with open(jf, 'r') as f:
for line in f:
i +=1

try:
proccess_record(line)
except Exception as e:
print e
print 'error processing line {}'.format(i)

if i > 10000:
f.close()
break

# We must construct an array in format (x, y) where by every period y we have
# total by period y indexes must be numbers so we get the y axis and
# create a list of indexes, every item in this list represent a period
# one period represents 3 months
period_list = []
keys = data_dict.keys()
keys.sort()
period_index = 0
with open('total_by_period.csv', 'w') as csvfile:
spamwriter = csv.writer(csvfile, delimiter=',')
#every period represents 3 monts
for n_index in range(len(keys)):
val = data_dict[keys[n_index]]
row = (period_index, str(val['total']))
spamwriter.writerow(row)
period_index += 3

def main():
parser = argparse.ArgumentParser()
args = parser.parse_args()

'total_by_period': total_by_period,
}

if __name__ == "__main__":
main()


## Generating Regression

We can now use octave to generate linear regression, first step is to load the data and create 2 vectos, one with x variables and another with y variables:

    % Load csv file

% Define x and y
x = data(:,1);
y = data(:,2);


Next step is to create plot function and call it:

    % Create a function to plot the data
function plotData(x,y)
plot(x,y,'rx','MarkerSize',8); % Plot the data
end

% Plot the data

plotData(x,y);

xlabel('Months since october 2011');

fprintf('Program paused. Press enter to continue.\n');

pause;


This funciton will generate the image below:

Next step is to calculate regression:

    % Count how many data points we have
m = length(x); % Add a column of all ones (intercept term) to x
X = [ones(m, 1) x];

% Calculate theta

theta = (pinv(X'*X))*X'*y


For our sample data theta values are [2.1368e+05, 2.3589e+03] this is our linear regression, Now we can plot it:

    hold on; % this keeps our previous plot of the training data visible
plot(X(:,2), X*theta, '-');
legend('Training data', 'Linear regression');
hold off % Do not put any more plots on this figure
pause;


The result image below:

## Tabulating some data

We can apply formula  y = theta[x] + theta[y]  to get some data:

    internet growth = theta[x] * month  + theta[y]
internet growth = 2.1368e+05 * month + 2.3589e+03

Months since October 2011 Number of users
48 (oct 2015) 10258998.9
57 (Jun 2016) 12182118.9
72 (oct 2017) 15387318.9