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Quadratic Regression

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Quadratic Regression

Study Guide

Key Definition

Quadratic regression is a statistical method used to model relationships with a parabolic curve. The equation is $y = ax^2 + bx + c$.

Important Notes

Quadratic regression fits a parabola, not a line.
It is used when data shows a curvilinear pattern.
The equation $y = ax^2 + bx + c$ describes the parabola.
The coefficients $a$, $b$, and $c$ are found using the least squares method.
Quadratic regression provides a more nuanced model than linear regression when appropriate.

Mathematical Notation

$X$ denotes the design matrix with columns [x^2, x, 1]

$β$ denotes the coefficient vector (a, b, c)^T

$X^T X$ is the Gram matrix in the normal equations

$X^T y$ is the response vector in the normal equations

Remember to use proper notation when solving problems

Why It Works

Quadratic regression is effective because it captures the non-linear relationship between variables using a $y = ax^2 + bx + c$ model.

Remember

Quadratic regression fits data with a parabolic trend using $y = ax^2 + bx + c$.

Quick Reference

Quadratic Equation:$y = ax^2 + bx + c$

Least Squares Method:Used to find $a$, $b$, $c$

Understanding Quadratic Regression

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Quadratic regression models data with a curve: $y = ax^2 + bx + c$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following represents a quadratic equation?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You want to model the path of a basketball shot using quadratic regression. Assume the data points form a parabolic path: $y = ax^2 + bx + c$. How do you determine $a$, $b$, and $c$?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given a set of data points that form a curve, how can you determine if quadratic regression is the best method to model the data?

Challenge Quiz

Single Choice Quiz

Advanced

Which method is used to find the best-fit parabola for quadratic regression?

Recap

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Review key concepts and takeaways