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
• \( b \) — Y-intercept

Explanation: The calculator finds the values of m and b that minimize the sum of the squared differences between the observed values and the values predicted by the linear model.

3. Importance of Linear Regression

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

4. Using the Calculator

Tips: Enter comma-separated x and y values. Both lists must be of equal length and contain at least 2 values each for the calculation to work.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between correlation and regression?
A: Correlation measures the strength of association between variables, while regression describes the nature of the relationship and can be used for prediction.

Q2: How many data points do I need?
A: At least 2 points are required to calculate a regression line, but more points provide a more reliable estimate.

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

Q4: Can I use this for non-linear relationships?
A: No, this calculator is for linear relationships only. For non-linear data, consider polynomial or other regression methods.

Q5: How accurate are the results?
A: Accuracy depends on how well your data fits a linear model. Check the residual plot to assess model fit.