1. What is Power Regression?

Power regression is a type of non-linear regression that models the relationship between two variables where one variable is proportional to the power of another. It follows the form y = a × x^b, where 'a' is the coefficient and 'b' is the exponent.

2. How Does the Calculator Work?

The calculator uses the power regression formula:

Where:

• \( y \) — Dependent variable (output value)
• \( a \) — Coefficient (scaling factor)
• \( x \) — Independent variable (input value)
• \( b \) — Exponent (power value)

Explanation: The equation describes how y changes as x changes, with the rate of change determined by the exponent b.

3. Applications of Power Regression

Details: Power regression is commonly used in physics (e.g., gravitational force), biology (allometric scaling), economics (production functions), and many other fields where relationships follow power laws.

4. Using the Calculator

Tips: Enter the coefficient (a), independent variable (x), and exponent (b). The calculator will compute the dependent variable (y). All values can be positive or negative (except when x=0 with b≤0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between power and exponential regression?
A: In power regression, the exponent is applied to x (y = a×x^b), while in exponential regression, the exponent is applied to the coefficient (y = a×b^x).

Q2: Can x be negative in power regression?
A: Yes, but only if b is an integer. For non-integer exponents, x must be positive.

Q3: How do I find the coefficients for a set of data points?
A: You would need to perform logarithmic transformation and linear regression on the log-transformed data.

Q4: What does a negative exponent mean?
A: A negative exponent means y decreases as x increases (inverse relationship).

Q5: What are common examples of power laws?
A: Examples include Kepler's laws of planetary motion, the Pareto principle (80/20 rule), and metabolic scaling laws.