1. What is Linear Regression?

Linear regression is a statistical method used to model the relationship between a dependent variable (y) and one or more independent variables (x). It finds the line of best fit through the data points using the equation y = a × x + b.

2. How Does the Calculator Work?

The calculator uses the linear regression equation:

Where:

• \( y \) — Dependent variable
• \( x \) — Independent variable
• \( a \) — Slope of the line
• \( b \) — Y-intercept
• \( r^2 \) — Coefficient of determination

Explanation: The calculator finds the best-fitting straight line through your data points by minimizing the sum of squared residuals.

3. Importance of Linear Regression

Details: Linear regression is widely used in statistics, machine learning, and scientific research to understand relationships between variables, make predictions, and identify trends in data.

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Ensure both lists have the same number of values. The calculator will compute the slope, intercept, and coefficient of determination.

5. Frequently Asked Questions (FAQ)

Q1: What does the slope (a) represent?
A: The slope represents the rate of change in the dependent variable (y) for each unit change in the independent variable (x).

Q2: What does the intercept (b) represent?
A: The intercept represents the value of y when x equals zero.

Q3: What does R² (coefficient of determination) mean?
A: R² indicates how well the regression line approximates the real data points, ranging from 0 to 1. Higher values indicate better fit.

Q4: How many data points are needed?
A: At least two data points are required, but more points provide a more reliable regression analysis.

Q5: Can this calculator handle non-linear data?
A: This calculator is designed for linear regression. For non-linear relationships, other regression methods would be more appropriate.