This calculator performs linear regression by calculating the slope, intercept, correlation coefficient (r), and R-squared (R²) values using your predictor and response data.

To use the calculator, provide a list of values for the predictor and the response, ensuring they are the same length, and then click the “Do Linear Regression” button.

**Regression Line: **y = ** + ****x**

**Goodness of fit:**

Correlation r =

R-Squared =

**Interpretation:**

The y-intercept ** represents the mean of the response variable when the predictor variable is zero.**

For each single unit increase in the predictor variable, there is an associated average change of ** in the response variable.**

The R-squared value tells us that **%** of the variation in the response variable is predictable from the predictor variable.

## Linear Regression Explanation

**Linear Regression** is a statistical method used to model the relationship between a dependent variable (response) and one or more independent variables (predictors). It is one of the simplest forms of regression analysis, commonly used to find the linear relationship between two variables.

### Key Concepts

**Predictor Variable (X)**: The independent variable used to predict the outcome.**Response Variable (Y)**: The dependent variable being predicted or explained.**Regression Line**: The straight line that best fits the data points on the plot.**Slope (m)**: Indicates how much the response variable changes for a one-unit change in the predictor variable.**Y-Intercept (b)**: The value of Y when the predictor variable (X) is zero.

### Linear Regression Formula

The relationship between the predictor and response variables in linear regression is expressed using the equation of a line:

where \( Y \) is the predicted value of the response, \( X \) is the predictor, \( m \) is the slope of the line, and \( b \) is the y-intercept.

### Steps to Perform Linear Regression

- Collect data for the predictor and response variables.
- Use the least squares method to estimate the slope and intercept of the regression line.
- Calculate the predicted values of the response variable for each value of the predictor.
- Evaluate the model's goodness of fit using metrics like the
**correlation coefficient (r)**and**R-squared (R²)**.

### Goodness of Fit

Linear regression models are evaluated based on how well they fit the data:

**Correlation Coefficient (r)**: Measures the strength of the relationship between the predictor and response variables. A value close to 1 or -1 indicates a strong linear relationship.**R-Squared (R²)**: Represents the proportion of the variance in the response variable that can be explained by the predictor variable(s). Higher values indicate a better fit.

### Further Reading

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.