Data Handling

Deterministic to Random: The Role of Probability in AI and Data Sc.

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

  Deterministic to Random: The Role of Probability in AI and Data Science Introduction An experiment refers to an operation or activity that can produce some well-defined outcome(s). Types of experiments: Deterministic Experiments Random (or Probabilistic) Experiments Deterministic Experiments These experiments have a fixed outcome or result, no matter how many times they are repeated […]

Deterministic to Random: The Role of Probability in AI and Data Sc. Read More »

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

Spearman’s Rank Correlation Coefficient Read More »

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

Derivation of Correlation Coefficient Property Read More »

Independence of Origin and Scale in Correlation Coefficient

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

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

  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

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

Karl Pearson’s Correlation Coefficient Numerical Example

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

  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,

Karl Pearson’s Correlation Coefficient Numerical Example Read More »

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}

Independence of Origin and Scale in Correlation Coefficient Read More »

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 =

Definition and Calculation of The Correlation Coefficient Video Read More »

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:

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

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

Understanding Correlation: Simplified Explanation Read More »

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

Covariance Made Simple: Unlocking the Secret of Relationships in Data Read More »

©Postnetwork-All rights reserved.