1. What is Linear Regression?

Linear regression is a statistical method that models the relationship between a dependent variable (y) and one or more independent variables (x) using a linear equation. It finds the line of best fit through the data points.

2. How Does the Calculator Work?

The calculator uses Python's scikit-learn library to perform linear regression:

Where:

• \( y \) — Dependent variable (output)
• \( x \) — Independent variable (input)
• \( m \) — Slope of the line
• \( b \) — Y-intercept

Explanation: The algorithm minimizes the sum of squared residuals to find the optimal values for m and b that best fit the data.

3. Importance of Regression Analysis

Details: Linear regression is widely used for prediction, forecasting, and understanding relationships between variables in various fields including economics, biology, and social sciences.

4. Using the Calculator

Tips: Enter comma-separated numerical values for both X and Y data. Ensure both arrays have the same number of elements for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is R-squared value?
A: R-squared measures how well the regression line approximates the real data points, ranging from 0 to 1 (higher is better).

Q2: Can I use this for multiple regression?
A: This calculator is designed for simple linear regression (one independent variable). Multiple regression requires additional inputs.

Q3: What assumptions does linear regression make?
A: Linear relationship, independence, homoscedasticity, and normal distribution of residuals.

Q4: How accurate are the results?
A: Accuracy depends on data quality and how well the linear model fits your data. Always validate with statistical tests.

Q5: What Python libraries are used?
A: This calculator uses numpy for numerical operations and scikit-learn's LinearRegression for the regression calculation.