Computer programming languages are often confusing for beginners, each with its own dialect and vernacular.

And every programming language has its own set of syntax and code to write. So how to chose a programming language to learn?

With computer programming languages ranging from 67-year-old Assembly language to the young Ruby language.

And you know what? Every language has its own presence in the computer programming world.

Even a brief glance at the list of programming languages available gives one a nightmare. But for now, knowing the top programming languages to learn will help.

But then which is the best computer programming languages for beginners? or which programming language to learn first?

I decided to shortlist the most commonly used computer programming languages for beginners and make a complete guide to it.

Hope the list helps you.

Check this computer programming deck for dummies before you read further about each of them in detail.

This will help you with a quick glance over each programming language.

• Assembly Language

  Learn more

  It was developed as a shorthand to machine language so that you don’t only have to remember 0’s and 1’s while coding.

  Today, Assembly languages are used to access a specialized processor or address critical performance issues by direct hardware manipulation.

  Typically, they are used in low-level embedded and real-time systems.

  If you want to program a processor, the assembly language may not be necessary, but it is invaluable.

  Major Organization Users: IBM, Apple

• C++ Language

  Learn more

  It is a middle-level, general purpose language. C++ brings in the feature of being object-oriented compared with its predecessor C.

  C++ is popular in areas where graphical representation is required like that for Windows and Macintosh.

  C++ has a rich function library and is a highly portable language.

  Here is beginners guide to C++ - C++ language tutorial

  Major Organization Users: Google, Mozilla, Firefox, Winamp, Adobe Software, Amazon, Lockheed Martin

• C Language

  Learn more

  It is a general-purpose programming language.

  C provides a construct to map assembly language to C and has been most popularly used for operations which had been previously coded in assembly languages, including operating systems.

  C is one of the most widely used languages and has been a great influence on its successors.

  Major Organization Users: Microsoft, Apple, Oracle, Cisco, Raytheon

• Objective C

  Learn more

  It is a general-purpose, object-oriented programming language that adds Smalltalk-style messaging in C language.

  Objective-C is one of the basic language used by Apple products and had been used in the development of iOS and OSX operating systems.

  Major Organization Users: Apple

• MATLAB

  Learn more

  It integrates computation and programming in an easy-to-use environment where most of the objectives are represented by mathematical notation.

  Matlab is a high-performance language and is typically used for mathematical computation and algorithm development.

  Major Organization Users: GE, Continental, Robert Bosch, Honeywell, Mercedes-Benz

• PERL

  Learn more

  It is a scripting language with syntax similar to C and has many features of UNIX. Programs written in Perl are called Perl script.

  Perl is an interpreted (not compiled) language that can optionally be compiled just before execution into either C code or cross-platform bytecode.

  Major Organizations Users: Apple, Yahoo, BBC, IMDB

• R

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  It is a dialect of S language. R language is used for statistical computing and graphics.

  R is commonly used by statisticians and data miners for statistical and analysis.

  R comes as a free software package and is available under GNU General public license.

  Major Organizations Users: Google, GE, Dropbox

• Visual Basic

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  It is a high-level language implemented on the .NET framework. VB was derived from BASIC, a user-friendly language designed for beginners.

  It enables the rapid application development (RAD) of graphical user interface (GUI) applications and access to databases using objects.

  Major Organizations Users: Microsoft

• PYTHON

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  It is another interpreted language on this list. Developed as a general purpose language.

  Python design emphasizes code readability and helps the user express in fewer lines of codes.

  Major Organizations Users: Google, Pinterest, Instagram, YouTube, DropBox, NASA, ESRI

• PHP

  Learn more

  It is a scripting language used by users to create dynamic pages, which can be used further for transferring and submitting information on the web.

  You can connect with servers, databases, and external websites based on IP address or information available.

  PHP is one of the most commonly used scripting languages by web developers.

  Major Organizations Users: Facebook, Google, GE, Wordpress

• Javascript

  Learn more

  It is a high-level programming language. Along with HTML and CSS, Javascript is one of the core languages in the development of World Wide Web content production.

  Most of the websites support javascript without needing plugins.

  Javascript is also used in the non-web-based application like PDF and desktop widgets.

  Major Organizations Users: WordPress, Soundcloud, Linkedin, Groupon, Yahoo

• C#

  Learn more

  It is another language in the list of C languages. C# (pronounced as C-Sharp) is an object-oriented and component-oriented programming language.

  C# is one of the programming languages developed for common language infrastructure.

  Developers working on Windows prefer C# for developing applications and it turns out that C# is a big competitor to Java.

  Major Organizations Users: Any company dealing extensively with Windows

• CSS

  Learn more

  CSS or Cascading style sheet is a style sheet language used for describing the presentation of documentation written in a markup language. Though often used for visual style up and user interface for HTML. CSS is a technology used by the most website to create visually engaging pages.

  Major Organizations Users: Apple, CyberCoders, Apex Systems

• Java

  Learn more

  It is often called the best programming language, amidst much debate. Java is a high-level language. It was intended to be “write once, run anywhere (WORA),” i.e., once the code is written, it could be used on any platform that uses Java. Java is used for client-server applications with more than 9 million developers using the platform.

  Major Organizations Users: V2COM, Eclipse Information Technologies, eBay, Eurotech

• Ruby

  Learn more

  It is one of the younger programming languages.

  Developed to increase productivity, Ruby is a server interpreted, non-compiled programming language.

  Ruby is used with Ruby on Rails for framework development.

  Major Organizations Users: Cybercoders, Amazon, EMC, Bloomberg

• SQL

  Learn more

  Though not considered a programming language listed under Alan Turing test of programming language, for now, SQL is one of the recruiter's favorite programming language.

  SQL, or Structured Query Language, is a special-purpose, domain-specific programming language used in programming and managing the database (DBMS).

  Often described as a declarative language, SQL also includes procedural elements.

  Despite being a standard in ANSI since 1986, most SQL code is not portable to among different database systems.

  Major Organizations Users: Facebook, Google, Adobe, Alcatel-Lucent

You can also read about these 13 rare and underrated programming skills to learn here

1. Get the whole setup ready before-hand

This is common sense. Get the whole setup ready. Fire-up your python editor before-hand. If you are writing your files in your local, create a virtual environment and activate it. Along with this, I would advise one other thing which might seem a bit controversial and counter-intuitive, and that is to use TDD. Use your favourite testing tool. I generally use pytest and have that “pip”-d in my virtual environment and start writing small test scripts. I have found that testing helps in clarity of thought, which helps in writing faster programs. Also, this helps in refactoring the code to make it faster. We will get to it later.

2. Get the code working first

People have their own coding styles. Use the coding style that you are most comfortable with. For the first iteration, make the code work, at least and make the submission. See if it passes for all the test cases. If it’s passing then, c'est fait. It's done. And you can move on to the next question.

In case its passing for some of the test cases, while failing for others, citing memory issues, then you know that there is still some work left.

3. Python Coding Tips

Strings:

Do not use the below construct.

s = ""
for x in somelist:
    s += some_function(x)

Instead use this

slist = [some_function(el) for el in somelist]
s = "".join(slist)

This is because in Python, str is immutable, so the left and right strings have to be copied into the new string for every pair of concatenation.

Language Constructs:

Functions: Make functions of your code and although procedural code is supported in Python, it's better to write them in functions.

def main():
    for i in xrange(10**8):
        pass

main()

is better than

for i in xrange(10**8):
    pass

This is because of the underlying CPython implementation. In short, it is faster to store local variables than globals. Read more in this SO post.

I would recommend you keep your procedural code as little as possible. You can use the following standard template.

def solution(args):
    # write the code
    pass

def main():
    # write the input logic to take the input from STDIN
    input_args = ""
    solution(input_args)

if __name__ == "__main__":
    main()

Use the standard library:

Use built-in functions and the standard library as much as possible. Therefore, instead of this:

newlist = []
for item in oldlist:
    newlist.append(myfunc(item))

Use this:

newlist = map(myfunc, oldlist)

There is also the list expressions or the generator expressions.

newlist = [myfunc(item) for item in oldlist]  # list expression
newlist = (myfunc(item) for item in oldlist)  # generator expression

Similarly, use the standard library, like itertools, as they are generally faster and optimized for common operations. So you can have something like permutation for a loop in just three lines of code.

>> import itertools
>>> iter = itertools.permutations([1,2,3])
>>> list(iter)
[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]

But if the containers are tiny, then any difference between code using libraries is likely to be minimal, and the cost of creating the containers will outweigh the gains they give.

Generators:

A Python generator is a function which returns a generator iterator (just an object we can iterate over) by calling yield. When a generator function calls yield, the "state" of the generator function is frozen; the values of all variables are saved and the next line of code to be executed is recorded until next() is called again. Generators are excellent constructs to reduce both the average time complexity as well as the memory footprint of the code that you have written. Just look at the following code for prime numbers.

def fib():
    a, b = 0, 1
    while 1:
        yield a
        a, b = b, a + b

So, this will keep on generating Fibonacci numbers infinitely without the need to keep all the numbers in a list or any other construct. Please keep in mind that you should use this construct only when you don't have any absolute need to keep all the generated values because then you will lose the advantage of having a generator construct.

4. Algorithms and Data structures

To make your code run faster, the most important thing that you can do is to take two minutes before writing any code and think about the data-structure that you are going to use. Look at the time complexity for the basic python data-structures and use them based on the operation that is most used in your code. The time complexity of the list taken from python wiki is shown below.

Similarly, keep on reading from all sources about the most efficient data structures and algorithms that you can use. Keep an inventory of the common data structures such as nodes and graphs and remember or keep a handy journal on the situations where they are most appropriate.

Writing fast code is a habit and a skill, which needs to be honed over the years. There are no shortcuts. So do your best and best of luck.

Reference:

stackoverflow.com: optimizing python code

dzone.com: 6 python performance tips

python wiki: Performance Tips

softwareengineering-stackexchange: lkndasldfn

quora: How do I speed up my Python code

python: list to string

monitis: python performance tips part 1

Introduction

“The best way to learn a new skill is by doing it!

This article is meant to help R users enhance their set of skills and learn Python for data science (from scratch). After all, R and Python are the most important programming languages a data scientist must know.

Python is a supremely powerful and a multi-purpose programming language. It has grown phenomenally in the last few years. It is used for web development, game development, and now data analysis / machine learning. Data analysis and machine learning is a relatively new branch in python.

For a beginner in data science, learning python for data analysis can be really painful. Why?

You try Googling "learn python," and you'll get tons of tutorials only meant for learning python for web development. How can you find a way then?

In this tutorial, we'll be exploring the basics of python for performing data manipulation tasks. Alongside, we'll also look how you do it in R. This parallel comparison will help you relate the set of tasks you do in R to how you do it in python! And in the end, we'll take up a data set and practice our newly acquired python skills.

Note: This article is best suited for people who have a basic knowledge of R language.

Table of Contents

1. Why learn Python (even if you already know R)
2. Understanding Data Types and Structures in Python vs. R
3. Writing Code in Python vs. R
4. Practicing Python on a Data Set

Why learn Python (even if you already know R)

No doubt, R is tremendously great at what it does. In fact, it was originally designed for doing statistical computing and manipulations. Its incredible community support allows a beginner to learn R quickly.

But, python is catching up fast. Established companies and startups have embraced python at a much larger scale compared to R.

According to indeed.com (from Jan 2016 to November 2016), the number of job postings seeking "machine learning python" increased much faster (approx. 123%) than "machine learning in R" jobs. Do you know why? It is because

1. Python supports the entire spectrum of machine learning in a much better way.
2. Python not only supports model building but also supports model deployment.
3. The support of various powerful deep learning libraries such as keras, convnet, theano, and tensorflow is more for python than R.
4. You don't need to juggle between several packages to locate a function in python unlike you do in R. Python has relatively fewer libraries, with each having all the functions a data scientist would need.

Understanding Data Types and Structures in Python vs. R

These programming languages understand the complexity of a data set based on its variables and data types. Yes! Let's say you have a data set with one million rows and 50 columns. How would these programming languages understand the data?

Basically, both R and Python have pre-defined data types. The dependent and independent variables get classified among these data types. And, based on the data type, the interpreter allots memory for use. Python supports the following data types:

1. Numbers – It stores numeric values. These numeric values can be stored in 4 types: integer, long, float, and complex.
   • Integer – Whole numbers such as 10, 13, 91, 102. Same as R's integer type.
   • Long – Long integers in octa and hexadecimal. R uses bit64 package for hexadecimal.
   • Float – Decimal values like 1.23, 9.89. Equivalent to R's numeric type.
   • Complex – Numbers like 2 + 3i, 5i. Rarely used in data analysis.
2. Boolean – Stores two values (True and False). R uses factor or character. Case-sensitive difference exists: R uses TRUE/FALSE; Python uses True/False.
3. Strings – Stores text like "elephant", "lotus". Same as R's character type.
4. Lists – Like R’s list, stores multiple data types in one structure.
5. Tuples – Similar to immutable vectors in R (though R has no direct equivalent).
6. Dictionary – Key-value pair structure. Think of keys as column names, values as data entries.

Since R is a statistical computing language, all the functions to manipulate data and reading variables are available inherently. On the other hand, python hails all the data analysis / manipulation / visualization functions from external libraries. Python has several libraries for data manipulation and machine learning. The most important ones are:

1. Numpy – Used for numerical computing. Offers math functions and array support. Similar to R’s list or array.
2. Scipy – Scientific computing in python.
3. Matplotlib – For data visualization. R uses ggplot2.
4. Pandas – Main tool for data manipulation. R uses dplyr, data.table.
5. Scikit Learn – Core library for machine learning algorithms in python.

In a way, python for a data scientist is largely about mastering the libraries stated above. However, there are many more advanced libraries which people have started using. Therefore, for practical purposes you should remember the following things:

1. Array – Similar to R's list, supports multidimensional data with coercion effect when data types differ.
2. List – Equivalent to R’s list.
3. Data Frame – Two-dimensional structure composed of lists. R uses data.frame; python uses DataFrame from pandas.
4. Matrix – Multidimensional structure of same class data. In R: matrix(); in python: numpy.column_stack().

Until here, I hope you've understood the basics of data types and data structures in R and Python. Now, let's start working with them!

Writing Code in Python vs. R

Let's use the knowledge gained in the previous section and understand its practical implications. But before that, you should install python using Anaconda's Jupyter Notebook. You can download here. Also, you can download other python IDEs. I hope you already have R Studio installed.

1. Creating Lists

In R:

my_list <- list('monday','specter',24,TRUE)
typeof(my_list)
[1] "list"

In Python:

my_list = ['monday','specter',24,True]
type(my_list)
list

Using pandas Series:

import pandas as pd
pd_list = pd.Series(my_list)
pd_list

0     monday
1    specter
2         24
3       True
dtype: object

Python uses zero-based indexing; R uses one-based indexing.

2. Matrix

In R:

my_mat <- matrix(1:10, nrow = 5)
my_mat
     [,1] [,2]
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10

# Select first row
my_mat[1,]

# Select second column
my_mat[,2]

In Python (using NumPy):

import numpy as np
a = np.array(range(10,15))
b = np.array(range(20,25))
c = np.array(range(30,35))
my_mat = np.column_stack([a, b, c])

# Select first row
my_mat[0,]

# Select second column
my_mat[:,1]

3. Data Frames

In R:

data_set <- data.frame(Name = c("Sam","Paul","Tracy","Peter"),
                       Hair_Colour = c("Brown","White","Black","Black"),
                       Score = c(45,89,34,39))

In Python:

data_set = pd.DataFrame({'Name': ["Sam","Paul","Tracy","Peter"],
                         'Hair_Colour': ["Brown","White","Black","Black"],
                         'Score': [45,89,34,39]})

Selecting columns:

In R:

data_set$Name
data_set[["Name"]]
data_set[1]

data_set[c('Name','Hair_Colour')]
data_set[,c('Name','Hair_Colour')]

In Python:

data_set['Name']
data_set.Name
data_set[['Name','Hair_Colour']]
data_set.loc[:,['Name','Hair_Colour']]

Practicing Python on a Data Set

import numpy as np
import pandas as pd
from sklearn.datasets import load_boston

boston = load_boston()

boston.keys()
['data', 'feature_names', 'DESCR', 'target']

print(boston['feature_names'])
['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO' 'B' 'LSTAT']

print(boston['DESCR'])

bos_data = pd.DataFrame(boston['data'])
bos_data.head()

bos_data.columns = boston['feature_names']
bos_data.head()

bos_data.describe()

# First 10 rows
bos_data.iloc[:10]

# First 5 columns
bos_data.loc[:, 'CRIM':'NOX']
bos_data.iloc[:, :5]

# Filter rows
bos_data.query("CRIM > 0.05 & CHAS == 0")

# Sample
bos_data.sample(n=10)

# Sort
bos_data.sort_values(['CRIM']).head()
bos_data.sort_values(['CRIM'], ascending=False).head()

# Rename column
bos_data.rename(columns={'CRIM': 'CRIM_NEW'})

# Column means
bos_data[['ZN','RM']].mean()

# Transform numeric to categorical
bos_data['ZN_Cat'] = pd.cut(bos_data['ZN'], bins=5, labels=['a','b','c','d','e'])

# Grouped sum
bos_data.groupby('ZN_Cat')['AGE'].sum()

# Pivot table
bos_data['NEW_AGE'] = pd.cut(bos_data['AGE'], bins=3, labels=['Young','Old','Very_Old'])
bos_data.pivot_table(values='DIS', index='ZN_Cat', columns='NEW_AGE', aggfunc='mean')

Summary

While coding in python, I realized that there is not much difference in the amount of code you write here; although some functions are shorter in R than in Python. However, R has really awesome packages which handle big data quite conveniently. Do let me know if you wish to learn about them!

Overall, learning both the languages would give you enough confidence to handle any type of data set. In fact, the best part about learning python is its comprehensive documentation available on numpy, pandas, and scikit learn libraries, which are sufficient enough to help you overcome all initial obstacles.

In this article, we just touched the basics of python. There's a long way to go. Next week, we'll learn about data manipulation in python in detail. After that, we'll look into data visualization, and the powerful machine learning library in python.

Do share your experience, suggestions, and questions below while practicing this tutorial!

Introduction

Recruiters in the analytics/data science industry expect you to know at least two algorithms: Linear Regression and Logistic Regression. I believe you should have in-depth understanding of these algorithms. Let me tell you why.

Due to their ease of interpretation, consultancy firms use these algorithms extensively. Startups are also catching up fast. As a result, in an analytics interview, most of the questions come from linear and Logistic Regression.

In this article, you'll learn Logistic Regression in detail. Believe me, Logistic Regression isn't easy to master. It does follow some assumptions like Linear Regression. But its method of calculating model fit and evaluation metrics is entirely different from Linear/Multiple regression.

But, don't worry! After you finish this tutorial, you'll become confident enough to explain Logistic Regression to your friends and even colleagues. Alongside theory, you'll also learn to implement Logistic Regression on a data set. I'll use R Language. In addition, we'll also look at various types of Logistic Regression methods.

Note: You should know basic algebra (elementary level). Also, if you are new to regression, I suggest you read how Linear Regression works first.

Table of Contents

1. What is Logistic Regression ?
2. What are the types of Logistic Regression techniques ?
3. How does Logistic Regression work ?
4. How can you evaluate Logistic Regression's model fit and accuracy ?
5. Practical - Who survived on the Titanic ?

What is Logistic Regression ?

Many a time, situations arise where the dependent variable isn't normally distributed; i.e., the assumption of normality is violated. For example, think of a problem when the dependent variable is binary (Male/Female). Will you still use Multiple Regression? Of course not! Why? We'll look at it below.

Let's take a peek into the history of data analysis.

So, until 1972, people didn't know how to analyze data which has a non-normal error distribution in the dependent variable. Then, in 1972, came a breakthrough by John Nelder and Robert Wedderburn in the form of Generalized Linear Models. I'm sure you would be familiar with the term. Now, let's understand it in detail.

Generalized Linear Models are an extension of the linear model framework, which includes dependent variables which are non-normal also. In general, they possess three characteristics:

1. These models comprise a linear combination of input features.
2. The mean of the response variable is related to the linear combination of input features via a link function.
3. The response variable is considered to have an underlying probability distribution belonging to the family of exponential distributions such as binomial distribution, Poisson distribution, or Gaussian distribution. Practically, binomial distribution is used when the response variable is binary. Poisson distribution is used when the response variable represents count. And, Gaussian distribution is used when the response variable is continuous.

Logistic Regression belongs to the family of generalized linear models. It is a binary classification algorithm used when the response variable is dichotomous (1 or 0). Inherently, it returns the set of probabilities of target class. But, we can also obtain response labels using a probability threshold value. Following are the assumptions made by Logistic Regression:

1. The response variable must follow a binomial distribution.
2. Logistic Regression assumes a linear relationship between the independent variables and the link function (logit).
3. The dependent variable should have mutually exclusive and exhaustive categories.

In R, we use glm() function to apply Logistic Regression. In Python, we use sklearn.linear_model function to import and use Logistic Regression.

Note: We don't use Linear Regression for binary classification because its linear function results in probabilities outside [0,1] interval, thereby making them invalid predictions.

What are the types of Logistic Regression techniques ?

Logistic Regression isn't just limited to solving binary classification problems. To solve problems that have multiple classes, we can use extensions of Logistic Regression, which includes Multinomial Logistic Regression and Ordinal Logistic Regression. Let's get their basic idea:

1. Multinomial Logistic Regression: Let's say our target variable has K = 4 classes. This technique handles the multi-class problem by fitting K-1 independent binary logistic classifier model. For doing this, it randomly chooses one target class as the reference class and fits K-1 regression models that compare each of the remaining classes to the reference class.

Due to its restrictive nature, it isn't used widely because it does not scale very well in the presence of a large number of target classes. In addition, since it builds K - 1 models, we would require a much larger data set to achieve reasonable accuracy.

2. Ordinal Logistic Regression: This technique is used when the target variable is ordinal in nature. Let's say, we want to predict years of work experience (1,2,3,4,5, etc). So, there exists an order in the value, i.e., 5>4>3>2>1. Unlike a multinomial model, when we train K -1 models, Ordinal Logistic Regression builds a single model with multiple threshold values.

If we have K classes, the model will require K -1 threshold or cutoff points. Also, it makes an imperative assumption of proportional odds. The assumption says that on a logit (S shape) scale, all of the thresholds lie on a straight line.

Note: Logistic Regression is not a great choice to solve multi-class problems. But, it's good to be aware of its types. In this tutorial we'll focus on Logistic Regression for binary classification task.

How does Logistic Regression work?

As we know, Logistic Regression assumes that the dependent (or response) variable follows a binomial distribution. Now, you may wonder, what is binomial distribution? Binomial distribution can be identified by the following characteristics:

1. There must be a fixed number of trials denoted by n, i.e. in the data set, there must be a fixed number of rows.
2. Each trial can have only two outcomes; i.e., the response variable can have only two unique categories.
3. The outcome of each trial must be independent of each other; i.e., the unique levels of the response variable must be independent of each other.
4. The probability of success (p) and failure (q) should be the same for each trial.

Y = ?o + ?1X + ?

In Logistic Regression, we use the same equation but with some modifications made to Y. Let's reiterate a fact about Logistic Regression: we calculate probabilities. And, probabilities always lie between 0 and 1. In other words, we can say:

1. The response value must be positive.
2. It should be lower than 1.

First, we'll meet the above two criteria. We know the exponential of any value is always a positive number. And, any number divided by number + 1 will always be lower than 1. Let's implement these two findings:

This is the logistic function.

Now we are convinced that the probability value will always lie between 0 and 1. To determine the link function, follow the algebraic calculations carefully. P(Y=1|X) can be read as "probability that Y =1 given some value for x." Y can take only two values, 1 or 0. For ease of calculation, let's rewrite P(Y=1|X) as p(X).

As you might recognize, the right side of the (immediate) equation above depicts the linear combination of independent variables. The left side is known as the log - odds or odds ratio or logit function and is the link function for Logistic Regression. This link function follows a sigmoid (shown below) function which limits its range of probabilities between 0 and 1.

Until here, I hope you've understood how we derive the equation of Logistic Regression. But how is it interpreted?

We can interpret the above equation as, a unit increase in variable x results in multiplying the odds ratio by ? to power ?. In other words, the regression coefficients explain the change in log(odds) in the response for a unit change in predictor. However, since the relationship between p(X) and X is not straight line, a unit change in input feature doesn't really affect the model output directly but it affects the odds ratio.

This is contradictory to Linear Regression where, regardless of the value of input feature, the regression coefficient always represents a fixed increase/decrease in the model output per unit increase in the input feature.

In Multiple Regression, we use the Ordinary Least Square (OLS) method to determine the best coefficients to attain good model fit. In Logistic Regression, we use maximum likelihood method to determine the best coefficients and eventually a good model fit.

Maximum likelihood works like this: It tries to find the value of coefficients (?o,?1) such that the predicted probabilities are as close to the observed probabilities as possible. In other words, for a binary classification (1/0), maximum likelihood will try to find values of ?o and ?1 such that the resultant probabilities are closest to either 1 or 0. The likelihood function is written as

How can you evaluate Logistic Regression model fit and accuracy ?

In Linear Regression, we check adjusted R², F Statistics, MAE, and RMSE to evaluate model fit and accuracy. But, Logistic Regression employs all different sets of metrics. Here, we deal with probabilities and categorical values. Following are the evaluation metrics used for Logistic Regression:

1. Akaike Information Criteria (AIC)

You can look at AIC as counterpart of adjusted r square in multiple regression. It's an important indicator of model fit. It follows the rule: Smaller the better. AIC penalizes increasing number of coefficients in the model. In other words, adding more variables to the model wouldn't let AIC increase. It helps to avoid overfitting.

Looking at the AIC metric of one model wouldn't really help. It is more useful in comparing models (model selection). So, build 2 or 3 Logistic Regression models and compare their AIC. The model with the lowest AIC will be relatively better.

2. Null Deviance and Residual Deviance

Deviance of an observation is computed as -2 times log likelihood of that observation. The importance of deviance can be further understood using its types: Null and Residual Deviance. Null deviance is calculated from the model with no features, i.e.,only intercept. The null model predicts class via a constant probability.

Residual deviance is calculated from the model having all the features.On comarison with Linear Regression, think of residual deviance as residual sum of square (RSS) and null deviance as total sum of squares (TSS). The larger the difference between null and residual deviance, better the model.

Also, you can use these metrics to compared multiple models: whichever model has a lower null deviance, means that the model explains deviance pretty well, and is a better model. Also, lower the residual deviance, better the model. Practically, AIC is always given preference above deviance to evaluate model fit.

3. Confusion Matrix

Confusion matrix is the most crucial metric commonly used to evaluate classification models. It's quite confusing but make sure you understand it by heart. If you still don't understand anything, ask me in comments. The skeleton of a confusion matrix looks like this:

As you can see, the confusion matrix avoids "confusion" by measuring the actual and predicted values in a tabular format. In table above, Positive class = 1 and Negative class = 0. Following are the metrics we can derive from a confusion matrix:

Accuracy - It determines the overall predicted accuracy of the model. It is calculated as Accuracy = (True Positives + True Negatives)/(True Positives + True Negatives + False Positives + False Negatives)

True Positive Rate (TPR) - It indicates how many positive values, out of all the positive values, have been correctly predicted. The formula to calculate the true positive rate is (TP/TP + FN). Also, TPR = 1 - False Negative Rate. It is also known as Sensitivity or Recall.

False Positive Rate (FPR) - It indicates how many negative values, out of all the negative values, have been incorrectly predicted. The formula to calculate the false positive rate is (FP/FP + TN). Also, FPR = 1 - True Negative Rate.

True Negative Rate (TNR) - It indicates how many negative values, out of all the negative values, have been correctly predicted. The formula to calculate the true negative rate is (TN/TN + FP). It is also known as Specificity.

False Negative Rate (FNR) - It indicates how many positive values, out of all the positive values, have been incorrectly predicted. The formula to calculate false negative rate is (FN/FN + TP).

F Score: F score is the harmonic mean of precision and recall. It lies between 0 and 1. Higher the value, better the model. It is formulated as 2((precision*recall) / (precision+recall)).