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Data Analytics Data Science education Mathematics Statistics

Deriving Least Squares Coefficients Using Tensor/Index Notation

Many textbooks when introducing ordinary least squares as a method to do regression (usually via introducing linear regression) don’t explain / derive the coefficients. Here, I explain how to do it using tensor/index notation.

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Biology Data Analytics Data Science Mathematics Statistics

Coronavirus Predictions

By: Dr. Ikjyot Singh Kohli I wrote an extensive script in R that takes the most recent data available for the number of new/confirmed COVID-19 cases per day by location and computes the probability using statistical learning that a selected location will observe a new COVID-19 case (probability of observing a non-zero daily percentage return). […]

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Basketball Mathematics NBA Sports Statistics

A Problem With Offensive Rating

Abstract: It is shown that the standard/common definition of team offensive rating/offensive efficiency implies that a team’s offensive rating increases as its opponent’s offensive rebounds increase, which, in principle, should not be the case. Over the past number of years, the advanced metric known as Offensive Rating has become the standard way of measuring a basketball […]

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Data Analytics Data Science Elections Mathematics Politics Statistics

The Probability of An Illegal Immigrant Committing a Crime In The United States

Trump has once again put The U.S. on the world stage this time at the expense of innocent children whose families are seeking asylum. The Trump administration’s justification is that:   “They want to have illegal immigrants pouring into our country, bringing with them crime, tremendous amounts of crime.”   I decided to try to […]

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Basketball Data Analytics Data Science Mathematics NBA NBA Playoffs Sports Statistics

The Risk of The 3-Point Shot

As more and more teams are increasing the number of threes they attempt based on some misplaced logical fallacy that this somehow leads to an efficient offense, we show below that it is in fact in a team’s opponent’s interest for a team to attempt as many three point shots as possible. Looking at this […]

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Basketball Data Analytics Data Science Mathematics Science Sports Statistics

An Equation to Predict NBA Playoff Probabilities

Based on a previous paper I wrote that used machine learning to determine the most relevant factors for teams making the NBA playoffs, I did some further analysis in an attempt to come up with an equation that outputs the probability of an NBA team making the playoffs in a given season. From the aforementioned […]

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Basketball Mathematics NBA Statistics

When is it optimal to shoot a 3-Point Shot

A very interesting result: computing payoffs of players, the following is a diagram that shows when it is optimal for a player to shoot a 2 point or a 3-point shot. One sees that it is hardly ever optimal for a player to shoot a 3-point shot, since the region corresponding to 3-point optimality is […]

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Basketball Chicago Bulls Data Analytics Data Science Mathematics NBA NBA Finals Sports Statistics

What if Michael Jordan Played in Today’s NBA?

By: Dr. Ikjyot Singh Kohli It seems that one cannot turn on ESPN or any YouTube channel nowadays without the ongoing debate of whether Michael Jordan is better than Lebron, what would happen if Michael Jordan played in today’s NBA, etc… However, I have not seen a single scientific approach to this question. Albeit, it […]

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Basketball Data Science Mathematics NBA NBA Playoffs Uncategorized

So, What’s Wrong with the Knicks?

By: Dr. Ikjyot Singh Kohli As I write this post, the Knicks are currently 12th in the Eastern conference with a record of 22-32. A plethora of people are offering the opinions on what is wrong with the Knicks, and of course, most of it being from ESPN and the New York media, most of […]

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Basketball Data Analytics Data Science Mathematics NBA NBA Finals NBA Playoffs Sports Statistics

Basketball Machine Learning Paper Updated 

I have now made a significant update to my applied machine learning paper on predicting patterns among NBA playoff and championship teams, which can be accessed here: arXiv Link .