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) by fitting a linear equation to observed data.

2. How Does the Calculator Work?

The calculator uses the least squares method to find the line of best fit:

Where:

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

Explanation: The calculator minimizes the sum of the squares of the residuals (the differences between observed and predicted values).

3. Importance of Linear Regression

Details: Linear regression is widely used in forecasting, trend analysis, and determining the strength of relationships between variables.

4. Using the Calculator

Tips: Enter comma-separated values for both X and Y variables. Ensure both lists have the same number of values. At least two data points are required.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between this and Desmos?
A: This provides the regression equation in the same format as Desmos but focuses specifically on simple linear regression.

Q2: How many data points do I need?
A: Minimum 2 points for a line, but more points provide a more reliable regression.

Q3: What does the R² value mean?
A: R² (coefficient of determination) shows how well the regression line fits the data (1 = perfect fit).

Q4: Can I use this for nonlinear data?
A: This calculator is for linear regression only. Nonlinear data may require polynomial or other regression types.

Q5: How accurate are the results?
A: Results are mathematically precise for the given data, but real-world interpretation depends on data quality.