Linear Regression by Hand

The basic idea behind linear regression is quite simple. In mathematical terms we want to predict a dependent variable Y using an independent variable X. By assuming that the two variables correlate in a linear fashion we can predict Y with a simple linear formula:

Linear equation by Author

(The wavy equal sign signifies “approximately”). Simply put, as soon as we know a bit about the relationship between the two coefficients, i.e. we have approximated the two coefficients **α **and β, we can (with some confidence) predict Y. Alpha α represents the intercept (value of y with f(x = 0)) and Beta β is the slope.

With the help of linear regression, we can answer a lot of questions; e.g.

• “Is the rise of sea level connected to rising temperatures?”,
• “How expensive will a house with 3 bedrooms be?”
• “How many items do we sell if we increase our marketing budget by 20%?”

#linear-regression #machine-learning-python #data-science #machine-learning #python

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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.

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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

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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.

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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

Hand Sanitizer in bulk - Get your effective hand sanitizer here

With the spread of various harmful virus globally causing immense distress and fatalities to human mankind, it has become absolutely essential for people to ensure proper and acute hygiene and cleanliness is maintained. To further add to the perennial hardship to save lives of people the recent pandemic of Covid-19 affected globally created the worst nightmare for people of all walks of life. Looking at the present crisis, it has become imperative for human beings to be encouraged to tackle this challenge with an everlasting strength to help protect oneself and their loved ones against the devastating effects of the virus. One thing that stands up between keeping all safe and vulnerable is by making sure that everybody attentively Hand wash periodically to help physically remove germs from the skin and getting rid of the live microbes.

The essence of apposite handwashing is based around time invested in washing and the amount of soap and water used. Technically, washing hands without soap is much less effective anyway. But incase a proper handwashing support system doesn’t become possible around, the usage of Effective Hand Sanitizer will certainly help fight to reduce the number of microbes on the surface of hands efficiently, eliminating most variants of harmful bacteria to settle.

The need has come about for Hand Sanitizer in bulk to save your daily life aptly maintaining a minimum of 60% alcohol - as per the CDC recommendations and approved by USFDA for its greater effectiveness. With the growing demand of people on the move the demand for easy to carry, small, and travel size worthy pouches that are also refillable once the product runs out is the need of the hour. To further make sure that human lives are well protected from these external viruses, it is mandatory for producer of effective Hand Sanitizer to evolve products circumspectly with ingredients that produce not just saving lives but with multiple benefits for people of all ages.

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Polynomial Regression — The “curves” of a linear model

The most glamorous part of a data analytics project/report is, as many would agree, the one where the Machine Learning algorithms do their magic using the data. However, one of the most overlooked part of the process is the preprocessing of data.

A lot more significant effort is put into preparing the data to fit a model on rather than tuning the model to fit the data better. One such preprocessing technique that we intend to disentangle is Polynomial Regression.

#data-science #machine-learning #polynomial-regression #regression #linear-regression