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:

• \( m \) — Slope of the line (change in y per unit change in x)
• \( b \) — Y-intercept (value of y when x = 0)

Calculation Steps:

1. Calculate the mean of x and y values
2. Compute the covariance of x and y
3. Compute the variance of x
4. Calculate slope (m) and intercept (b)

3. Importance of Regression Analysis

Details: Regression analysis helps understand relationships between variables, predict outcomes, and test scientific hypotheses about causal relationships.

4. Using the Calculator

Tips: Enter comma-separated x and y values. Ensure equal number of points in both sets. Values should be numeric.

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum number of data points needed?
A: At least 2 points are required, but more points provide more reliable results.

Q2: How accurate is this method?
A: Least squares regression provides the best linear unbiased estimate when assumptions are met.

Q3: What if my data isn't linear?
A: Linear regression works best for linear relationships. Consider transformations or nonlinear models for other patterns.

Q4: How do I interpret the slope?
A: The slope represents how much y changes for each 1-unit change in x.

Q5: What is R-squared?
A: R-squared measures how well the regression line fits the data (0-1 scale, higher is better fit).