1. What is Quadratic Regression?

Quadratic regression is a process of finding the equation of a parabola that best fits a set of data. It produces a second-degree polynomial equation in the form y = ax² + bx + c.

2. How Does the Calculator Work?

The calculator uses the quadratic equation:

Where:

• \( a \) — Quadratic coefficient (determines parabola's width and direction)
• \( b \) — Linear coefficient
• \( c \) — Constant term (y-intercept)
• \( x \) — Independent variable input
• \( y \) — Dependent variable output

Explanation: This calculator computes the y-value for a given x-value using pre-determined coefficients from quadratic regression analysis.

3. Importance of Quadratic Regression

Details: Quadratic regression is essential for modeling relationships where the rate of change is not constant. It's widely used in physics, engineering, economics, and biological sciences to model curved relationships.

4. Using the Calculator

Tips: Enter the coefficients (a, b, c) from your quadratic regression analysis and the x-value for which you want to predict y. The calculator will compute the corresponding y-value on the parabola.

5. Frequently Asked Questions (FAQ)

Q1: How do I get the coefficients (a, b, c)?
A: Use statistical software or a graphing calculator (like Casio) in regression mode with your dataset to calculate these values.

Q2: What does a negative 'a' coefficient mean?
A: A negative 'a' means the parabola opens downward, indicating a maximum point. Positive 'a' means it opens upward with a minimum point.

Q3: How accurate is quadratic regression?
A: Accuracy depends on how well a quadratic model fits your data. Check the R² value from your regression analysis to assess goodness-of-fit.

Q4: Can I use this for extrapolation?
A: Be cautious with extrapolation beyond your data range, as quadratic functions can diverge quickly outside the observed range.

Q5: What's the difference from linear regression?
A: Quadratic regression can model curved relationships (one bend) while linear regression only models straight-line relationships.