Quadratic Regression Calculator

The quadratic regression calculator can be used to fit a quadratic equation to a set of input data points.

The quadratic regression calculator will find a line of best fit according to the value of the order parameter.

The fit is found using the least squares method. The least squares method finds a regression fit that minimizes the distance between input x values and observed y values.

Statisticians sometimes describe quadratic regression as a type of linear regression. Fitting a quadratic equation to a set of input points requires solving a set of linear equations.

Quadratic regression model

This quadratic regression calculator fits a quadratic regression model to input predictor variables.

The equation below shows the second-order quadratic regression formula.

Where $y$ is the predicted response variable and x is the measured predictor variable. $a$, $b$ and $c$ are the calculated regression coefficients.

What Is the Difference Between Quadratic Regression and Multiple Linear Regression

Quadratic regression is used to find a quadratic line of best fit for one response variable based on one predictor variable. Statisticians sometimes call this a form of simple linear regression because there is one predictor variable, one response variable and the regression equations are linear.

Multiple linear regression is used to find a line of best fit for one response variable based on the values of one or more predictor variables.

You could model a car's fuel efficiency based on its weight using quadratic regression. You could model a car's fuel efficiency based on its weight and its horsepower using multiple linear regression.

What Is the Difference Between the Correlation Coefficient and Regression Fit

The correlation coefficient is used to measure how strong the linear relationship is between two variables. It is a number between -1 and 1.

Quadratic regression is used to fit a function to the relationship between input x and y values.

If two variables have a non-linear relationship (e.g. they are best fit with $y=x^2$), then the quadratic regression calculator might find a good fit, but the two variables might have a poor Pearson's correlation coefficient.