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). The simple linear regression equation y = mx + c represents a straight line that best fits the data points.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( m \) — Slope of the regression line
• \( c \) — Y-intercept of the regression line
• \( Cov(x,y) \) — Covariance between x and y variables
• \( Var(x) \) — Variance of x variable
• \( \bar{x} \) — Mean of x values
• \( \bar{y} \) — Mean of y values

Explanation: The calculator finds the line that minimizes the sum of squared differences between observed and predicted y values.

3. Importance of Regression Analysis

Details: Linear regression is widely used in statistics, economics, social sciences, and machine learning for prediction, forecasting, and understanding relationships between variables.

4. Using the Calculator

Tips: Enter comma-separated x and y values. Ensure both lists have the same number of elements. The calculator will compute the regression equation y = mx + c.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between correlation and regression?
A: Correlation measures the strength of relationship, while regression models the relationship to make predictions.

Q2: How many data points are needed for reliable regression?
A: Generally, more data points provide more reliable results. A minimum of 5-10 points is recommended for basic analysis.

Q3: What does the R-squared value represent?
A: R-squared measures how well the regression line approximates the real data points (0-100% of variance explained).

Q4: Can this calculator handle multiple regression?
A: This calculator handles simple linear regression (one independent variable). Multiple regression requires more complex calculations.

Q5: What are the assumptions of linear regression?
A: Key assumptions include linear relationship, independence of observations, homoscedasticity, and normal distribution of residuals.