1. What is Linear Regression (ax+b)?

Linear regression (ax+b form) 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. The "least squares" method minimizes the sum of the squares of the residuals.

2. How Does the Calculator Work?

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

Where:

• \( a \) — Slope of the line
• \( b \) — Y-intercept
• \( n \) — Number of data points
• \( \sum xy \) — Sum of x*y products
• \( \sum x \) — Sum of x values
• \( \sum y \) — Sum of y values
• \( \sum x^2 \) — Sum of squared x values

3. Importance of Least Squares Method

Details: The least squares method provides the best linear unbiased estimator (BLUE) of the regression coefficients under the Gauss-Markov theorem. It's widely used in statistics, economics, and sciences.

4. Using the Calculator

Tips: Enter comma-separated x and y values (must be equal in number). The calculator will compute the slope (a), intercept (b), and full regression equation.

5. Frequently Asked Questions (FAQ)

Q1: Why is it called "least squares"?
A: Because it minimizes the sum of the squares of the residuals (differences between observed and predicted values).

Q2: How is this different from y=a+bx form?
A: It's the same mathematically, just different notation. TI-84 calculators use ax+b form by default.

Q3: What's a good R² value?
A: R² values closer to 1 indicate better fit, but interpretation depends on context. There's no universal "good" value.

Q4: Can I use this for nonlinear data?
A: Linear regression assumes a linear relationship. For nonlinear data, consider transformations or nonlinear regression.

Q5: How many data points do I need?
A: More points give more reliable results. At least 5-10 points are recommended for meaningful analysis.