Calculator
Results
Data Source and Methodology
All calculations are rigorously based on standard statistical formulas for linear regression. For further insights, please refer to "Introduction to Linear Regression Analysis" by Douglas C. Montgomery.
The Formula Explained
y = mx + b
where m is the slope, b is the y-intercept, and r is the correlation coefficient.
Glossary of Variables
- Input Data X: The independent variable data set.
- Input Data Y: The dependent variable data set.
- Slope (m): The rate of change in Y for a unit change in X.
- Intercept (b): The value of Y when X is zero.
- Correlation Coefficient (r): A measure of the strength and direction of a linear relationship.
How It Works: A Step-by-Step Example
Suppose you have the data sets X: [1, 2, 3] and Y: [2, 4, 6]. The calculator will compute the slope (m) as 2, the intercept (b) as 0, and the correlation coefficient (r) as 1, indicating a perfect linear relationship.
Frequently Asked Questions (FAQ)
What is linear regression used for?
Linear regression is used to model the relationship between a dependent variable and one or more independent variables.
Can I use this calculator for non-linear data?
No, this calculator is specifically designed for linear relationships. Non-linear models require different techniques.
What do the slope and intercept represent?
The slope represents the change in the dependent variable for a unit change in the independent variable, while the intercept is the value of the dependent variable when the independent variable is zero.
How accurate are the results?
The results are highly accurate for properly formatted and valid input data.
Do I need to preprocess the data?
Ensure your data is clean and free from outliers for the best results.