Correlation and Regression Analysis – UGCNET17

Data Visualization

0/7

Frequency Polygon

Difference Between Histogram and Frequency Polygon

Relative Frequency Distribution

Cumulative Frequency Table

Box and Whiskers : IQR

Contingency Table

Statistics

0/8

Method of Least Square : Regression Analysis

Assumptions Regarding the Error Term in Regression

Demand Forecasting

Types of Reliability in Research

ISO 9000 Series Standards

Lean Manufacturing

5S Lean Methodology

Concept, Measures of Central Tendency and Dispersion,

0/8

**Contingency Table (Cross-Tabulation Table)

**Measures of Central Tendency: Mean, Median & Mode

**Standard Deviation

**Karl Pearson’s Coefficient of Variation

**Positional Averages (Positional Means)

**Mathematical Averages (Mathematical Means)

Population Variance v/s Sample variance

Measures of Dispersion

Probability Distribution – Binomial, Poisson, Normal, and Exponential

0/8

Different Distributions

Normal Distribution Characteristics

Normal Distribution Example

**Binomial Distribution

**Poisson Distribution / Queing Theory

Poisson distribution

Exponential Distribution

Binomial Distribution

Data Collection & Questionnaire Design

Sampling: Concept, Process, and Techniques

0/2

**Sampling Methods

–research process

Hypothesis Testing: Procedure

0/2

**Hypothesis Testing

–Type I & Type II Errors

T, Z, F, Chi-square tests

0/3

Types of Statistical Tests

Chi-Square Goodness of Fit Test

Limitation of Chi Square Test

Correlation and Regression Analysis

0/4

Correlation Coefficient

Regression Coefficient

Relationship Between Correlation Coefficient and Regression Coefficient

Correlation and Regression Analysis

Operations Management Basics

0/6

EOQ: Economic Order Quantity

Process Mapping Symbols

Key Figures in Operations Management

Operations Management: Role and Scope

0/3

–Introduction

Facility Location and Layout: Site Selection and Analysis, Layout Design and Process

Facility Location and Layout

0/3

Plant Layout Design

Data Collection Method

Enterprise Resource Planning: ERP Modules, ERP Implementation

Scheduling: Loading, Sequencing, and Monitoring

0/6

**Line Balancing

**Inspection Process and Types

Scheduling: Johnson’s Rule

Johnson’s rule example

Quality Management and Statistical Quality Control, Quality Circles, Total Quality Management – KAIZEN, Benchmarking, Six Sigma

0/5

Benchmarking Generations

Sequence of Activities involved in Quality Circle Development

Quality Control Tools

ISO 9000 Series Standards

Operation Research: Transportation, Queuing Decision Theory, PERT/CPM.

0/8

**Assignment: Complete Enumeration Method

–VAM: Vogel’s Approximation Method

**North-West Corner Method

**PERT: Program Evaluation and Review Technique

**CPM: Critical Path Method

**Queue Discipline

Transportation

0/4

Tranportation Foundations

Framework/Algortihm to Solve Transportation Problems

LCM: Least Cost Method

What is ERP (Enterprise Resource Planning)?

Final Evaluation

0/1

Rapid Fire : Business Statistics and Operations Management

Unit VIII: Business Statistics and Operations Management

For a given set of pair data, the correlation and regression coefficients have been calculated as being equal to r, byx and bxy respectively. Now, each of values in the x series is divided by 4. What effect does it have on each of their coefficients?

✅ Correct Answer: There is no change in r but byx changes to 4byx and bxy changes to bxy/4.

📘 Explanation:

We have a dataset where:

$r$ = Correlation coefficient
$b_{y x}$ = Regression coefficient of Y on X
$b_{x y}$ = Regression coefficient of X on Y

Now, each value in the x-series is divided by 4. Let’s analyze the effect.

1. Effect on Correlation Coefficient ()

The correlation coefficient () is a unit-free measure of the relationship between X and Y.
Scaling X by dividing by 4 does not affect .

🔹 Conclusion:

2. Effect on Regression Coefficient $b_{y x}$ (Regression of Y on X)

The formula for $b_{y x}$ is:

$b_{y x} = [r \times σ ^{y}^{] / σ x}$

(standard deviation of X) is divided by 4, so the denominator decreases by a factor of 4.
Since division in the denominator leads to an increase in value, $b_{y x}$ is multiplied by 4.

🔹 Conclusion: $b_{y x'} = 4 \times b_{y x}$

2. Effect on Regression Coefficient $b_{x y}$ (Regression of X on Y)

The formula for $b_{x y}$ is:

Since $σ_{x}$ is divided by 4, the numerator decreases by a factor of 4.
This means $b_{x y}$ is divided by 4.

🔹 Conclusion: $b_{x y'} = b ^{x y}$

✅ Final Answer:

Coefficient	Effect
(Correlation Coefficient)	No Change
$b_{y x}$ (Regression of Y on X)	Multiplied by 4
$b_{x y}$ (Regression of X on Y)	Divided by 4