Scatter Plot Calculator
Create scatter plots, analyze correlations, and find linear regression lines
Data Input
Scatter Plot
Statistical Analysis
Correlation Analysis
Linear Regression
Descriptive Statistics
Interpretation
Correlation: No significant linear relationship between variables.
R²: 0.0% of the variance in Y is explained by X.
Calculation Steps
Step 1: Calculate means: x̄ = 0.0000, ȳ = 0.0000
Step 2: Calculate correlation coefficient using Pearson's formula
r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)² × Σ(yi - ȳ)²] = 0.0000
Step 3: Calculate regression line using least squares method
Slope: m = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)² = 0.0000
Intercept: b = ȳ - m×x̄ = 0.0000
Step 4: Calculate R² (coefficient of determination) = 0.0000
Example Datasets
Strong Positive Correlation
Height vs Weight example:
Negative Correlation
Price vs Sales example:
Correlation Strength Guide
Key Concepts
Correlation ≠ Causation
Strong correlation doesn't imply one variable causes the other
R-squared (R²)
Proportion of variance in Y explained by X
Linear Regression
Best-fit line through data points using least squares
Outliers
Points far from the trend can affect correlation
Understanding Scatter Plots
What is a Scatter Plot?
A scatter plot is a graph that displays the relationship between two quantitative variables. Each point represents an observation with coordinates (x, y) corresponding to the values of the two variables.
When to Use Scatter Plots
- •Explore relationships between continuous variables
- •Identify patterns, trends, or correlations
- •Detect outliers in your dataset
- •Visualize data before statistical analysis
Key Statistical Measures
Correlation Coefficient (r)
Measures the strength and direction of linear relationship between variables. Range: -1 to +1.
R-squared (R²)
Coefficient of determination. Shows the proportion of variance in the dependent variable explained by the independent variable.
Linear Regression
Best-fit line through the data points using the least squares method. Equation: y = mx + b
Real-World Applications
Business & Economics
Sales vs advertising spend, price vs demand, employee satisfaction vs productivity.
Science & Research
Temperature vs chemical reaction rate, dose vs response, age vs bone density.
Education & Psychology
Study time vs test scores, class size vs achievement, anxiety vs performance.