Research and Development

Spearman’s Rank Correlation Coefficient

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

Spearman’s Rank Correlation Coefficient Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Need for Spearman’s Rank Correlation Coefficient In many cases, the relationship between variables is not linear, making Pearson’s correlation coefficient unsuitable. Spearman’s Rank Correlation measures the strength and direction of a monotonic relationship between two variables. It is […]

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Derivation of Correlation Coefficient Property

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

  Derivation of the Correlation Coefficient Data Science and A.I. Lecture Series   Problem Statement Objective: Derive the formula for the correlation coefficient \( r(X, Y) \): \[ r(X, Y) = \frac{\sigma_X^2 + \sigma_Y^2 – \sigma_{X-Y}^2}{2 \sigma_X \sigma_Y}. \] Definitions: \( \sigma_X^2 \): Variance of \( X \). \( \sigma_Y^2 \): Variance of \( Y

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Independence of Origin and Scale in Correlation Coefficient

Karl Pearson’s Correlation −1≤r(X,Y)≤1

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  Prove \( -1 \leq r(X, Y) \leq 1 \) for Karl Pearson’s Correlation Coefficient Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Problem Statement Prove that: \[ -1 \leq r(X, Y) \leq 1 \] The correlation coefficient \( r(X, Y) \) is a measure of the linear relationship between

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Karl Pearson’s Correlation Coefficient Numerical Example

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  Karl Pearson’s Correlation Coefficient Learn the step-by-step process of finding the correlation coefficient in statistics. Problem Statement Find the Karl Pearson’s coefficient of correlation between \(X\) and \(Y\) for the given data: \[ \begin{aligned} X &: 6, 2, 4, 9, 1, 3, 5, 8 \\ Y &: 13, 8, 12, 15, 9, 10, 11,

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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.

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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

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  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 Explained: Change of Origin vs. Scale Made Simple!

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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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