This calculator performs **Quadratic Regression** and produces an equation for the line of best fit for the provided predictor and response values.

The equation takes the form: \( y = a + bx + cx^2 \)

To use the calculator, provide a list of values for the predictor and the response, ensuring they are the same length, and then click the "Do Quadratic Regression" button.

**Quadratic Regression Equation:**

y = a + (b)x + (c)x^{2}

## Quadratic Regression and Coefficient Interpretation

The **Quadratic Regression** fits an equation in the form:

This model is useful when the change in the response variable \(Y\) is related to both \(X\) and \(X^2\), allowing for non-linear trends in the data. It can model curved relationships, unlike simple linear regression.

### Interpretation of Coefficients

- \(a\) represents the intercept, or the value of \(Y\) when \(X = 0\).
- \(b\) is the linear coefficient, representing how \(Y\) changes with \(X\).
- \(c\) is the quadratic coefficient, representing the curvature in the relationship between \(X\) and \(Y\).

### Caveats and Conditions

**Non-linear Trends:**Quadratic regression is suited for non-linear trends. If the relationship is not quadratic, this model may not fit well.**Outliers:**Large outliers can significantly affect the fitted curve and coefficients.**Overfitting:**Quadratic models, being more complex than linear models, may lead to overfitting if applied to small datasets or noisy data.

### Further Reading

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.