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) using a linear equation. The TI-84 calculator uses the least squares method to find the best-fitting line.

2. How Does the Calculator Work?

The calculator uses the linear regression equation:

Where:

• \( y \) — Dependent variable (predicted value)
• \( a \) — Y-intercept (constant term)
• \( b \) — Slope (regression coefficient)
• \( x \) — Independent variable (input value)

Explanation: The equation represents a straight line where 'a' is where the line crosses the y-axis and 'b' represents the steepness of the line.

3. Importance of Linear Regression

Details: Linear regression is widely used for prediction and forecasting, understanding relationships between variables, and in machine learning as a basic predictive algorithm.

4. Using the Calculator

Tips: Enter the intercept (a), slope (b) from your regression analysis, and the x value for which you want to predict y. The calculator will compute the corresponding y value on the regression line.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from TI-84's built-in function?
A: This calculator uses the same formula but provides a simpler interface for quick calculations once you have the regression coefficients.

Q2: What do the a and b values represent?
A: 'a' is the y-intercept (expected y value when x=0) and 'b' is the slope (change in y per unit change in x).

Q3: How accurate are the predictions?
A: Accuracy depends on how well the linear model fits your data. Check the R² value from your regression analysis.

Q4: Can I use this for multiple regression?
A: No, this calculator is for simple linear regression with one independent variable only.

Q5: What if my relationship isn't linear?
A: For non-linear relationships, consider other regression models like polynomial, logarithmic, or exponential regression.