Pearson Correlation Coefficient Calculator | पियर्सन सहसंबंध गुणांक कैलकुलेटर – Direct & Indirect Methods

Pearson Correlation Coefficient Calculator | पियर्सन सहसंबंध गुणांक कैलकुलेटर – Direct & Indirect Methods

Pearson Correlation Coefficient Calculator

पियर्सन सहसंबंध गुणांक कैलकुलेटर

Calculate Pearson’s r using Direct Method & Indirect Method with Step-by-Step Solutions

Direct Method
Indirect Method

Note: Both lists must have the same number of values.

Calculating… Please wait
Direct Method: \( r = \frac{\Sigma d_x d_y}{\sqrt{\Sigma d_x^2 \times \Sigma d_y^2}} \)
Indirect Method: \( r = \frac{\Sigma dxdy – \frac{\Sigma dx \times \Sigma dy}{N}}{\sqrt{\Sigma d^2 x – \frac{(\Sigma dx)^2}{N} \times \sqrt{\Sigma d^2 y – \frac{(\Sigma dy)^2}{N}}}} \)

Correlation Interpretation Guide

r Value Strength Interpretation
±0.9 to ±1.0 Very Strong Perfect linear relationship
±0.7 to ±0.9 Strong High degree of correlation
±0.5 to ±0.7 Moderate Moderate correlation
±0.3 to ±0.5 Weak Low degree of correlation
0 to ±0.3 Very Weak Little to no correlation
← Scroll to view full table →

Complete Guide to Pearson Correlation Coefficient

What is Pearson Correlation Coefficient?

The Pearson Correlation Coefficient (r) is a statistical measure that calculates the strength and direction of the linear relationship between two variables. Developed by Karl Pearson, this coefficient ranges from -1 to +1, where:

  • +1: Perfect positive linear relationship
  • -1: Perfect negative linear relationship
  • 0: No linear relationship

Direct Method vs Indirect Method

Direct Method: This method calculates deviations from actual means. It’s straightforward but can be computationally intensive with large datasets or decimal numbers.

Indirect Method (Assumed Mean Method): This method uses assumed means to simplify calculations. It reduces computational complexity and is preferred for larger datasets.

Applications of Pearson Correlation

  • Finance: Analyze correlation between stocks for portfolio diversification
  • Healthcare: Study relationship between drug dosage and patient recovery
  • Education: Examine correlation between study hours and exam scores
  • Marketing: Analyze relationship between ad spend and sales revenue
  • Quality Control: Study correlation between temperature and product quality

How to Calculate in Excel

In Microsoft Excel, you can use the CORREL function:

=CORREL(array1, array2)
Example: =CORREL(A2:A100, B2:B100)

Understanding r² (Coefficient of Determination)

The square of Pearson’s r (r²) represents the proportion of variance in the dependent variable that can be explained by the independent variable. For example:

  • r = 0.8 → r² = 0.64 → 64% of variation in Y explained by X
  • r = 0.5 → r² = 0.25 → 25% of variation in Y explained by X

Common Practice Problems

Try these practice problems to master Pearson correlation calculation:

  1. Calculate correlation between study hours (X: 2,4,6,8,10) and exam scores (Y: 65,75,85,95,100)
  2. Find correlation between temperature (X: 20,25,30,35,40) and ice cream sales (Y: 50,75,100,125,150)
  3. Determine correlation between advertising spend (X: 1000,2000,3000,4000,5000) and sales (Y: 15000,25000,35000,45000,55000)

Limitations and Considerations

  • Pearson correlation measures only linear relationships
  • Outliers can significantly affect the correlation coefficient
  • Correlation does not imply causation
  • Requires interval or ratio scale data
  • Assumes homoscedasticity (constant variance)

Related Calculators

  • Mean Calculator
  • Standard Deviation Calculator
  • Linear Regression Calculator
  • Spearman Rank Correlation Calculator
  • Hypothesis Testing Calculator
Correlation Results
Pearson’s r
–
Coefficient of Determination (r²)
–
Mean of X (X̄)
–
Mean of Y (Ȳ)
–
Interpretation
Enter data and click “Calculate Correlation” to see interpretation
Calculation Table
📊 Table includes all calculations 📱 Scroll horizontally on mobile
Table will appear here after calculation
← Scroll horizontally to view full table →
Step-by-Step Solution
Steps:
  1. Enter your X and Y values
  2. Select calculation method
  3. Click “Calculate Correlation”
  4. View detailed step-by-step solution

पियर्सन सहसंबंध गुणांक | Pearson Correlation Coefficient Calculator – Complete Guide

Free Pearson Correlation Calculator Online | Direct & Indirect Methods | Step-by-Step Solutions | Pearson’s r Formula | Correlation Coefficient Calculation

Pearson Correlation Calculator Correlation Coefficient Formula Statistics Calculator Online Pearson’s r Calculation

What is Pearson Correlation Coefficient? | पियर्सन सहसंबंध गुणांक क्या है?

Pearson Correlation Coefficient (Pearson’s r) is a statistical measure that calculates the strength and direction of the linear relationship between two continuous variables. Developed by Karl Pearson in 1895, it’s one of the most widely used correlation measures in statistics, research, and data analysis.

पियर्सन सहसंबंध गुणांक (Pearson’s r) एक सांख्यिकीय माप है जो दो सतत चरों के बीच रैखिक संबंध की शक्ति और दिशा की गणना करता है। कार्ल पियर्सन द्वारा 1895 में विकसित, यह सांख्यिकी, शोध और डेटा विश्लेषण में सबसे व्यापक रूप से उपयोग किए जाने वाले सहसंबंध उपायों में से एक है।

Key Features of Pearson Correlation Coefficient:

-1 to +1

Range of Values

मानों की सीमा

+1

Perfect Positive Correlation

पूर्ण सकारात्मक संबंध

-1

Perfect Negative Correlation

पूर्ण नकारात्मक संबंध

0

No Linear Correlation

कोई रैखिक संबंध नहीं

Pearson Correlation Calculator Features | पियर्सन सहसंबंध कैलकुलेटर विशेषताएं

✓ Direct Method Calculation

Calculate using actual means with formula:
\( r = \frac{\Sigma d_x d_y}{\sqrt{\Sigma d_x^2 \times \Sigma d_y^2}} \)

Perfect for small datasets and exact calculations

✓ Indirect Method Calculation

Calculate using assumed mean with formula:
\( r = \frac{\Sigma dxdy – \frac{\Sigma dx \times \Sigma dy}{N}}{\sqrt{\Sigma d^2 x – \frac{(\Sigma dx)^2}{N} \times \sqrt{\Sigma d^2 y – \frac{(\Sigma dy)^2}{N}}}} \)

Ideal for large datasets and decimal values

✓ Step-by-Step Solutions

Detailed calculation steps with formulas

Complete calculation table with all values

Interpretation guide for correlation values

Perfect for students and researchers

Pearson Correlation Formula | पियर्सन सहसंबंध सूत्र

Direct Method Formula:

\[ r = \frac{\Sigma (X_i – \bar{X})(Y_i – \bar{Y})}{\sqrt{\Sigma (X_i – \bar{X})^2 \Sigma (Y_i – \bar{Y})^2}} \]

Indirect Method Formula (Assumed Mean):

\[ r = \frac{\Sigma dxdy – \frac{(\Sigma dx)(\Sigma dy)}{n}}{\sqrt{[\Sigma dx^2 – \frac{(\Sigma dx)^2}{n}][\Sigma dy^2 – \frac{(\Sigma dy)^2}{n}]}} \]

Where | जहाँ:

  • \( r \) = Pearson correlation coefficient
  • \( X_i \) = Individual X values
  • \( Y_i \) = Individual Y values
  • \( \bar{X} \) = Mean of X values
  • \( \bar{Y} \) = Mean of Y values
  • \( dx = X – A \) (A = Assumed mean for X)
  • \( dy = Y – B \) (B = Assumed mean for Y)
  • \( n \) = Number of data pairs
  • \( \Sigma \) = Summation symbol

How to Calculate Pearson Correlation Coefficient | पियर्सन सहसंबंध गुणांक की गणना कैसे करें

Step-by-Step Calculation Process:

Step 1: Direct Method Calculation

  1. Calculate mean of X values: \( \bar{X} = \frac{\Sigma X}{n} \)
  2. Calculate mean of Y values: \( \bar{Y} = \frac{\Sigma Y}{n} \)
  3. Find deviations: \( d_x = X – \bar{X} \), \( d_y = Y – \bar{Y} \)
  4. Calculate \( d_x^2 \), \( d_y^2 \), and \( d_x d_y \)
  5. Find sums: \( \Sigma d_x^2 \), \( \Sigma d_y^2 \), \( \Sigma d_x d_y \)
  6. Apply formula: \( r = \frac{\Sigma d_x d_y}{\sqrt{\Sigma d_x^2 \times \Sigma d_y^2}} \)

Step 2: Indirect Method Calculation

  1. Choose assumed means A (for X) and B (for Y)
  2. Calculate \( dx = X – A \), \( dy = Y – B \)
  3. Find \( dx^2 \), \( dy^2 \), and \( dx \times dy \)
  4. Calculate sums: \( \Sigma dx \), \( \Sigma dy \), \( \Sigma dx^2 \), \( \Sigma dy^2 \), \( \Sigma dxdy \)
  5. Apply formula: \[ r = \frac{\Sigma dxdy – \frac{(\Sigma dx)(\Sigma dy)}{n}}{\sqrt{[\Sigma dx^2 – \frac{(\Sigma dx)^2}{n}][\Sigma dy^2 – \frac{(\Sigma dy)^2}{n}]}} \]

Step 3: Interpretation of Results

  • ±0.90 to ±1.00: Very strong correlation
  • ±0.70 to ±0.89: Strong correlation
  • ±0.50 to ±0.69: Moderate correlation
  • ±0.30 to ±0.49: Weak correlation
  • 0.00 to ±0.29: Very weak or no correlation

Applications of Pearson Correlation | पियर्सन सहसंबंध के अनुप्रयोग

📊 Research & Statistics

  • Academic research studies
  • Statistical analysis
  • Data science projects
  • Market research analysis
  • Scientific experiments

💼 Business & Finance

  • Stock market analysis
  • Portfolio diversification
  • Sales forecasting
  • Marketing analytics
  • Risk assessment

🏥 Healthcare & Medicine

  • Clinical trials analysis
  • Drug effectiveness studies
  • Patient data analysis
  • Epidemiological research
  • Medical statistics

🎓 Education & Psychology

  • Educational research
  • Psychological testing
  • Student performance analysis
  • Test validation studies
  • Behavioral research

Direct Method vs Indirect Method Comparison | प्रत्यक्ष vs अप्रत्यक्ष विधि तुलना

Feature Direct Method Indirect Method
Accuracy High accuracy High accuracy
Calculation Complexity More complex Simpler calculations
Best For Small datasets Large datasets
Decimal Handling Can be messy Handles well
Computational Time More time Less time
Manual Calculation Difficult Easier

How to Use Pearson Correlation Calculator | पियर्सन सहसंबंध कैलकुलेटर कैसे उपयोग करें

Simple 4-Step Process:

1

Enter Data

Input X and Y values separated by commas

Example: 10, 20, 30, 40, 50

2

Select Method

Choose Direct or Indirect Method

Based on your data type

3

Calculate

Click Calculate button

Get instant results

4

View Results

See correlation coefficient

With interpretation guide

FAQ – Frequently Asked Questions | सामान्य प्रश्न

Q1: What is Pearson Correlation Coefficient?

Pearson Correlation Coefficient (r) measures linear relationship between two variables, ranging from -1 to +1.

Q2: How to interpret Pearson correlation value?

±0.9-1.0: Very strong, ±0.7-0.9: Strong, ±0.5-0.7: Moderate, ±0.3-0.5: Weak, 0-0.3: Very weak.

Q3: What is the difference between Direct and Indirect methods?

Direct uses actual means, Indirect uses assumed means to simplify calculations for large datasets.

Q4: How to calculate Pearson correlation in Excel?

Use =CORREL(array1, array2) function in Excel for Pearson correlation calculation.

Q5: What is coefficient of determination (r²)?

r² represents proportion of variance in dependent variable explained by independent variable.

Related Calculators | संबंधित कैलकुलेटर

Pearson Correlation Coefficient Calculator

Free Online Pearson Correlation Calculator

Calculate Pearson’s r with our free online calculator. Get step-by-step solutions using both direct method and indirect method. Perfect for statistics students, researchers, and data analysts.

Pearson Correlation Calculator Features

  • Direct Method Calculation
  • Indirect Method Calculation
  • Step-by-Step Solutions
  • Detailed Calculation Tables
  • Correlation Interpretation Guide
  • Free Online Tool
  • No Registration Required
  • Download Results Option

How to Calculate Pearson Correlation

Our Pearson correlation calculator makes it easy to calculate correlation coefficient between two variables. Just enter your X and Y values, select calculation method, and get instant results with detailed steps.

Pearson Correlation Formula

The Pearson correlation coefficient formula measures linear relationship between variables. Use our calculator to apply the formula: r = Σ[(xi – x̄)(yi – ȳ)] / √[Σ(xi – x̄)² Σ(yi – ȳ)²]

Correlation Coefficient Interpretation

Learn how to interpret Pearson correlation values. Our calculator provides interpretation guide for correlation strength: very strong, strong, moderate, weak, or very weak correlation.

Statistics Calculator Online

Free statistics calculator for correlation analysis. Calculate Pearson correlation coefficient for research, academic projects, data analysis, and statistical studies.

Note: This calculator is for educational purposes. For professional statistical analysis, consult with a qualified statistician.

© 2024 Pearson Correlation Calculator | Free Online Statistics Tool | Pearson’s r Calculator | Correlation Coefficient Calculator

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