1. What is Least Squares Regression?

Least squares regression is a statistical method used to find the line of best fit for a set of data points by minimizing the sum of the squares of the vertical deviations from each data point to the line.

2. How Does the Calculator Work?

The calculator uses the least squares method to find the regression line:

Where:

• \( \hat{y} \) — Predicted y value
• \( \beta_0 \) — Y-intercept
• \( \beta_1 \) — Slope of the line
• \( Cov(x,y) \) — Covariance between x and y
• \( Var(x) \) — Variance of x
• \( \bar{x}, \bar{y} \) — Means of x and y values

3. Importance of Regression Analysis

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

4. Using the Calculator

Tips: Enter comma-separated x and y values of equal length. The calculator will compute the regression line equation, slope, and intercept.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between correlation and regression?
A: Correlation measures the strength of association, while regression describes the relationship with an equation for prediction.

Q2: How many data points do I need?
A: At least two points are needed, but more points increase reliability of the regression line.

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

Q4: What does R-squared represent?
A: R-squared measures the proportion of variance in y explained by x (0 to 1).

Q5: Can I use this for non-linear relationships?
A: No, this is for linear relationships only. Other regression types are needed for non-linear data.