Logistic Regression

This is a follow up tutorial on my previous post linear regression on my road to understanding machine learning. As a summary, linear regression is where we try to fit a straight line to a bunch of data having an independent variable such as time against a dependent variable in our case the sales profit. From the straight line, can we then predict at a certain time what the profit will be like.

Logistic Regression is concerned with classification. From our previous post, I can say that sales profit below K400 is bad(0) according to our business rules and above K400 is good(1). In other words, what we a doing is separating our points to two discrete values, it is either good or bad profit and in binary 0 0r 1.

days,sales,productivity
0,0,0
5,100,0
10,300,0
15,4000,1
20,8000,1
25,9000,1
        

To view our data points, let's plot them.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn import linear_model as lm

#Linear Regression is simply fitting a straight line to the data, a best fit line.

#read file csv
df=pd.read_csv('sales_classification.csv')

#plot the data

plt.xlabel('sales')
plt.ylabel('productivity')
plt.scatter(df.sales,df.productivity,color="red",marker="+")
plt.show()        

The resulting plot.

With linear regression, the formula for the straight line is shown below but for logistic regression, the curve that we are trying to draw is a sigmoid curve as shown;

##Linear
y= mx + c

##Logistic
y(x) =   1 / 1 + e-x(e raised to power of -x) where e is Euler's number
        

And doing the actual fitting, training and prediction. A prediction for a K399 and K10000 is done yielding the classifications.

x_sales=df[["sales"]]
y_productivity=df[["productivity"]]
model = lm.LogisticRegression()
# #train the model or fitting a line to the data
model.fit(x_sales,y_productivity)
#make the prediction for K399 sales profit
print("Predicted class of a sales profit of K399 ..",model.predict([[399]]))
print("Predicted class of a sales profit of K10000 ..",model.predict([[10000]]))
        

The results.

Predicted class of a sales profit of K399 .. [0]

Predicted class of a sales profit of K10000 .. [1]        

Note: Please checkout DigitalSreeni's youtube channel if I am confusing you.