# Tag: linearmodels

The book Learn Data Science with R covers minimal theory, practical examples, and projects. It starts with an explanation of the underlying concepts of data science, followed by implementing them in R language. Learn linear regression, logistic regression, random forests, and other machine learning algorithms. The hands-on projects provide a detailed step-by-step guide for analyzing and predicting data.
The book covers the following topics –
R Language
Statistics and Mathematics

Or how to make sure the airplane’s altitude is not negative.

Linear Regression is usually the first algorithm that people learn for Machine Learning and Data Science. Linear Regression is a linear model that assumes a linear relationship between the input variables (`X`) and the single output variable (`y`). In general, there are two cases:

• Single Variable Linear Regression: it models the relationship between a single input variable (single feature variable) and a single output variable.
• Multi-Variable Linear Regression (also known as Multivariate Linear Regression): it models the relationship between multiple input variables (multiple features variables) and a single output variable.

This algorithm is common enough that Scikit-learn has this functionality built-in with `LinearRegression()`.

This is often referred to as the “Kernel Trick”. The above procedure allows us to fit linear decision boundaries in high-dimensional feature spaces without explicitly calculating all of the features in said high-dimensional space into an explicit Feature Matrix X. This is even the case when our high-dimensional feature space of interest is infinitely dimensional! There is a considerable volume of literature on Mercers Theorem and Reproducing Kernel Hilbert Spaces (RKHS) that mathematically supports the above statement, but it’s beyond the scope of this article. Rather I’m going to provide an intuitive explanation supporting this claim based on simple linear algebra and dot products:

Say we have a Feature Matrix X with n observations and p features (i.e.

## Exploring statistics using Calculus

Accurate pricing is essential to protecting an insurance company’s bottom line. Pricing directly impacts the near-term profitability and long-term health of an insurer’s book of business. The ability to charge more accurate premiums helps the company mitigate risk and maintain a competitive advantage, which, in turn, also benefits consumers.

The methods actuaries use to arrive at accurate pricing have evolved. In earlier days, they were limited to univariate approaches. The minimum bias approach proposed by Bailey and Simon in the 1960s was gradually adopted over the next 30 years. The later introduction of Generalized Linear Models (GLM) significantly expanded the pricing actuary’s toolbox. … Read more...

Section-3 of the image-2 (above), gives us the data related to parameter estimates or coefficients for our regression model. Let’s understand this in detail.

Please see below table 2.3 representing this part for quick reference.

Our regression model equation is give by : y-pred=B0 + B1*X1 + B2*X2..

Specifically for this model, y-pred = 0.209 + 0.001 * X

## Coefficients:

Parameter estimates OR regression coefficients are the values of B1, B2 .. etc. They can be thought of as the weightage or importance of independent variables (i.e.

## Using Bayesian Linear Regression to account for uncertainty

Linear regression is among the most frequently used — and most useful — modelling tool.

While no form of regression analysis can ever approximate reality, it can do quite a good job at both making predictions for the dependent variable and determining the extent to which each independent variable impacts the dependent variable, i.e. the size and significance of each coefficient.

However, traditional linear regression can have shortcomings in that this method cannot really account for uncertainty in the estimates.

However, Bayesian linear regression can serve as a solution to this problem — by providing many different estimates of the coefficient values through repeated simulations.

## The only trick you’ll need to forever understand MLR coefficients.

Generally, I am not a fan of the terminology Artificial intelligence (AI). It is too broad, and non-technical minded people imagine that AI is a singular entity that makes decisions independently. Additionally, because AI is a popular term, I have seen examples where companies advertise themselves using AI when they are actually “just” using linear regression. Throughout the last 80 years, the term has gotten a bad rap in pop culture because of all the doomsday science-fiction stories and movies. Countless times we have seen science-fiction turning into science-faction, and with the advent of the text generator GPT-3 by OpenAI, it sure looks like we are on track.

Learn how and why LASSO works

Source: towardsdatascience.com

Time series forecasting is a very fascinating task. However, build a machine-learning algorithm to predict future data is trickier than expected. The hardest thing to handle is the temporal dependency present in the data. By their nature, time-series data are subject to shifts. This may result in temporal drifts of various kinds which may become our algorithm inaccurate.

One of the best tips I recommend, when modeling a time series problem, is to stay simple. Most of the time the simpler solutions are the best ones in terms of accuracy and adaptability. They are also easier to maintain or embed and more persistent to possible data shifts.

## The Question

My project question is “How does the number of field goal attempts affect the field goal percentage?

During the timeouts of NBA games, we can always hear the coach shouting at the players, “Keep shooting!

It’s believed by most NBA professionals that one can finally find his rhythm if he keeps shooting the ball to the basket even though he’s freezing cold now. Actually, the underlying assumption is that the increase in the number of field goal attempts can positively affect the field goal made (and finally increase the field goal percentage).

Some players even complain that they are not performing well in terms of the field goal percentage just because they are not allowed to shoot as many as the superstars do on court.

## An implementation of a neural network using PySpark for a binary class prediction use-case

### Overview

As a student of data science, I recently learned how to model variable interactions using Ordinary Least Squares (OLS) linear regression. It struck me as strange that the common advice to avoid the Dummy Variable Trap when analyzing categorical variables is to simply drop the first column based on the alpha-numeric category labels.

My intuition was that it must matter to some degree which column we choose to drop. And if it does matter, dropping a column because its label comes first seems very arbitrary and not especially scientific.… Read more...

To get a little more insight, lets run an info and we will get below info in figure 3.

• We have 2 text fields ie. Country and Status
• Fields such as alcohol, hepatitis B etc. have null values which we will need to resolve
• The column names need some work
`df.info()`

The names are not great to work with, so lets rename some of the columns. Then convert object fields to numbers as we cannot work with text . Finally, lets move Y into its own array and drop it from `df`. The result of this steep is that `df` is our feature set and only contains numbers, while `y` is our result set.

It is often the case that a dataset contains significant outliers – or observations that are significantly out of range from the majority of other observations in our dataset. Let us see how we can use robust regressions to deal with this issue.

I described in another tutorial how we can run a linear regression in R. However, this does not account for the outliers in our data. So, how can we solve this?

Plots

A useful way of dealing with outliers is by running a robust regression, or a regression that adjusts the weights assigned to each observation in order to reduce the skew resulting from the outliers.

KDnuggets Home » News » 2021 » Aug » Top Stories » Top Stories, Aug 2-8: 3 Reasons Why You Should Use Linear Regression Models Instead of Neural Networks; Bootstrap a Modern Data Stack in 5 minutes with Terraform ( 21:n30 )

## Systems of Linear Equations

In this article, you’ll be able to use what you learned about vectors and matrices, and linear combinations (respectively Chapter 05, 06 and 07 of Essential Math for Data Science). This will allow you to convert data into systems of linear equations. At the end of this chapter (in Essential Math for Data Science), you’ll see how you can use systems of equations and linear algebra to solve a linear regression problem.

Linear equations are formalizations of the relationship between variables. Take the example of a linear relationship between two variables x and y defined by the following equation:

You can represent this relationship in a Cartesian plane:

``````# create x and y vectors
x = np.linspace(-2,``````

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