Artificial Intelligence

Independence of Origin and Scale in Correlation Coefficient

Independence of Origin and Scale in Correlation Coefficient

Artificial Intelligence, Data Handling, Machine Learning, Probability and Statistics, Research and Development, Statistics /

Independence of Origin and Scale in Karl Pearson’s Correlation Coefficient Definition of Correlation Coefficient The correlation coefficient \( r(X, Y) \) is defined as: \[ r(X, Y) = \frac{\text{Cov}(X, Y)}{\sqrt{\text{Var}(X) \cdot \text{Var}(Y)}}. \] Covariance: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n (x_i – \bar{X})(y_i – \bar{Y}) \] Variance of \( X \): \[ \text{Var}(X) = \frac{1}{n} […]

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Definition and Calculation of The Correlation Coefficient Video

Artificial Intelligence, Data Handling, Machine Learning, Probability and Statistics, Research and Development, Statistics /

The Definition and Calculation of The Correlation Coefficient Data Science and A.I. Lecture Series   1. Definition of Correlation Coefficient The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is denoted by r, and it ranges from -1 to +1: r = +1: Perfect positive correlation. r =

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Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality Data Science and A.I.

Artificial Intelligence, Data Handling, Research and Development, Statistics /

Why is Covariance Bounded? The Power of Cauchy-Schwarz Inequality   Covariance and Standard Deviation Definitions: Sample Covariance: \[ \text{Cov}(X, Y) = \frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})(Y_i – \bar{Y}) \] Sample Standard Deviations: \[ \sigma_X = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (X_i – \bar{X})^2}, \quad \sigma_Y = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (Y_i – \bar{Y})^2} \] Cauchy-Schwarz Inequality The Cauchy-Schwarz inequality states:

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Understanding Correlation: Simplified Explanation

Artificial Intelligence, Data Handling, Probability and Statistics, Research and Development, Statistics /

  Understanding Correlation: A Simplified Explanation Welcome to this post in the Data Science and A.I. Lecture Series by Bindeshwar Singh Kushwaha from PostNetwork Academy! Today, we’ll dive into correlation—a crucial concept in data science and statistics. — What is Correlation? In simple terms, correlation measures the strength and direction of the relationship between two

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Covariance

Covariance: A Numerical Example

Artificial Intelligence, Machine Learning, Probability and Statistics, Research and Development, Statistics /

  Covariance: A Numerical Example Data Science and A.I. Lecture Series   Problem Statement and Table of Deviations Example: Calculate the covariance between the age of husband and wife of the following seven couples. Data: Age of Husband \( X \): 35, 34, 40, 43, 56, 20, 38 Age of Wife \( Y \): 32,

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Covariance

Covariance Made Simple: Unlocking the Secret of Relationships in Data

Artificial Intelligence, Data Handling, Machine Learning, Maths, Probability and Statistics, Statistics /

  Covariance Made Simple: Unlocking the Secret of Relationships in Data Welcome to Postnetwork Academy! In this post, Bindeshwar explains the concept of covariance, a fundamental tool in statistics and data science. Covariance helps us understand how two variables move together—whether they increase, decrease, or show no relationship at all. What You’ll Learn in This

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Covariance Explained: Change of Origin vs. Scale Made Simple!

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Maths, Probability and Statistics, Research and Development, Statistics /

Covariance Explained: Change of Origin vs. Scale Made Simple! Welcome to PostNetwork Academy’s Data Science and AI Lecture Series! In this post, we’ll explore the mathematical concept of covariance and how it behaves under changes of origin and scale. Let’s break it down step by step. Theorem: Covariance Independence We aim to prove that: Covariance

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Covariance Simplified: Learn It Once, Understand It Forever! Video #|109 Data Science and A.I.

Covariance Simplified: Learn It Once, Understand It Forever

Artificial Intelligence, Data Handling, Machine Learning, Probability and Statistics, Research and Development, Statistics /

Covariance Simplified: Learn It Once, Understand It Forever! Covariance measures the relationship between two random variables \(X\) and \(Y\). The formula for covariance is: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n (x_i – \bar{X})(y_i – \bar{Y}) \] Expanding the terms: \[ \text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^n \textcolor{red}{x_i y_i} – \textcolor{green}{x_i \bar{Y}} – \textcolor{blue}{\bar{X} y_i} + \textcolor{red}{\bar{X}

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Bivariate Distribution

Bivariate Distribution Made Simple: From Definition to Covariance Calculation

Artificial Intelligence, Data Handling, Machine Learning, Probability and Statistics, Research and Development, Statistics /

  Introduction Welcome to the Data Science and AI Lecture Series! In this post, we will simplify the concept of Bivariate Distribution and demonstrate how to calculate Covariance. These are fundamental concepts in statistics for understanding the relationship between two variables. Let’s dive into it! Bivariate Distribution Made Simple: From Definition to Covariance Calculation Author:

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Moments and Pearson’s Coefficient Simplified | Data Science & A.I. Lecture Series

Artificial Intelligence, Data Handling, Machine Learning, Mathematics, Probability and Statistics, Statistics /

  Introduction Welcome to the Data Science and A.I. Lecture Series presented by PostNetwork Academy. In this session, we’ll focus on key statistical concepts: moments about the mean, skewness, and kurtosis. These concepts are essential in understanding data distribution characteristics and play a significant role in data science, artificial intelligence, and statistical analysis. In this

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