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# Linear Regression from Scratch: Statistical Approach

Hello world! Welcome back to my post! Today I wanna share another project that I just done: **a **linear regression. But wait, this one is different! Usually I use either Scikit-Learn or Keras module to do machine learning stuff, but now, I decided to solve this regression problem using statistical approach. That’s essentially why we do not need optimization algorithm for this task — which makes this project relatively simple compared to other machine learning tasks.

Note: I share the full code used in this project at the end of this article.

#mathematics #python #linear-regression #ai #statistics

1601139600

## Linear Regression from Scratch: Statistical Approach

Hello world! Welcome back to my post! Today I wanna share another project that I just done: **a **linear regression. But wait, this one is different! Usually I use either Scikit-Learn or Keras module to do machine learning stuff, but now, I decided to solve this regression problem using statistical approach. That’s essentially why we do not need optimization algorithm for this task — which makes this project relatively simple compared to other machine learning tasks.

Note: I share the full code used in this project at the end of this article.

#mathematics #python #linear-regression #ai #statistics

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## A Deep Dive into Linear Regression

Let’s begin our journey with the truth — machines never learn. What a typical machine learning algorithm does is find a mathematical equation that, when applied to a given set of training data, produces a prediction that is very close to the actual output.

Why is this not learning? Because if you change the training data or environment even slightly, the algorithm will go haywire! Not how learning works in humans. If you learned to play a video game by looking straight at the screen, you would still be a good player if the screen is slightly tilted by someone, which would not be the case in ML algorithms.

However, most of the algorithms are so complex and intimidating that it gives our mere human intelligence the feel of actual learning, effectively hiding the underlying math within. There goes a dictum that if you can implement the algorithm, you know the algorithm. This saying is lost in the dense jungle of libraries and inbuilt modules which programming languages provide, reducing us to regular programmers calling an API and strengthening further this notion of a black box. Our quest will be to unravel the mysteries of this so-called ‘black box’ which magically produces accurate predictions, detects objects, diagnoses diseases and claims to surpass human intelligence one day.

We will start with one of the not-so-complex and easy to visualize algorithm in the ML paradigm — Linear Regression. The article is divided into the following sections:

1. Need for Linear Regression

2. Visualizing Linear Regression

3. Deriving the formula for weight matrix W

4. Using the formula and performing linear regression on a real world data set

Note: Knowledge on Linear Algebra, a little bit of Calculus and Matrices are a prerequisite to understanding this article

Also, a basic understanding of python, NumPy, and Matplotlib are a must.

## 1) Need for Linear regression

Regression means predicting a real valued number from a given set of input variables. Eg. Predicting temperature based on month of the year, humidity, altitude above sea level, etc. Linear Regression would therefore mean predicting a real valued number that follows a linear trend. Linear regression is the first line of attack to discover correlations in our data.

Now, the first thing that comes to our mind when we hear the word linear is, a line.

Yes! In linear regression, we try to fit a line that best generalizes all the data points in the data set. By generalizing, we mean we try to fit a line that passes very close to all the data points.

But how do we ensure that this happens? To understand this, let’s visualize a 1-D Linear Regression. This is also called as Simple Linear Regression

#calculus #machine-learning #linear-regression-math #linear-regression #linear-regression-python #python

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## Regression: Linear Regression

Machine learning algorithms are not your regular algorithms that we may be used to because they are often described by a combination of some complex statistics and mathematics. Since it is very important to understand the background of any algorithm you want to implement, this could pose a challenge to people with a non-mathematical background as the maths can sap your motivation by slowing you down.

In this article, we would be discussing linear and logistic regression and some regression techniques assuming we all have heard or even learnt about the Linear model in Mathematics class at high school. Hopefully, at the end of the article, the concept would be clearer.

**Regression Analysis **is a statistical process for estimating the relationships between the dependent variables (say Y) and one or more independent variables or predictors (X). It explains the changes in the dependent variables with respect to changes in select predictors. Some major uses for regression analysis are in determining the strength of predictors, forecasting an effect, and trend forecasting. It finds the significant relationship between variables and the impact of predictors on dependent variables. In regression, we fit a curve/line (regression/best fit line) to the data points, such that the differences between the distances of data points from the curve/line are minimized.

#regression #machine-learning #beginner #logistic-regression #linear-regression #deep learning

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## 5 Regression algorithms: Explanation & Implementation in Python

Take your current understanding and skills on machine learning algorithms to the next level with this article. What is regression analysis in simple words? How is it applied in practice for real-world problems? And what is the possible snippet of codes in Python you can use for implementation regression algorithms for various objectives? Let’s forget about boring learning stuff and talk about science and the way it works.

#linear-regression-python #linear-regression #multivariate-regression #regression #python-programming

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## A Complete Guide to Linear Regression for Beginners

What is supervised learning? In supervised learning, you have an input-output pair. And you will try to map the given input to output by training the input-output pair.

Another type of machine learning algorithm is unsupervised learning, in this, you don’t have an output variable. You will try to group the input variables by their similarities.

What is Regression? Regression is a statistical process of estimating the relationship between a dependant variable and several independent variables.

In other words, it can be said that linear regression suggests that the output variable can be represented as a linear combination of the input variables.

Linear Regression Example

Depending upon the number of input variables, linear regression can be classified into simple and multiple linear regression. If the number of input variables is one, then it is called simple linear regression.

Simple Linear Regression Formula

If there is more than one input variable, then it is called multiple linear regression.

Multiple Linear Regression Formula

In this blog post, I will be discussing simple linear regression.