Polynomial Regression Calculator

More about this Polynomial Regression Calculator so you can have a deeper perspective of the results that will be provided by this calculator.

Polynomial Regression is very similar to Simple Linear Regression, only that now one predictor and a certain number of its powers are used to predict a dependent variable \(Y\).

What is the Polynomial Regression Model

So, one of the big questions here is wow do you write a polynomial regression equation. The polynomial linear regression model is written as

\[ Y = \displaystyle \beta_0 + \beta_1 X + \beta_2 X^2 + ... + \beta_n X^n + \epsilon\]

where \(\epsilon\) is the error term that has the property of being normally distributed with mean 0 and constant variance \(\epsilon ~ N(0, \sigma^2)\).

After providing sample values for the predictor \(X\) and the response variable \(Y\), estimates of the population slope coefficients are obtained by minimizing the total sum of squared errors. The estimated model is expressed as:

\[ \hat Y = \displaystyle \hat\beta_0 + \hat\beta_1 X + \hat\beta_2 X^2 + ... + \hat\beta_n X^n\]

How is polynomial regression calculated?

The procedure is the same as with most regression procedures: You have a dependent variable \(Y\) which you want to predict in terms of one or more predictors.

In this case, the independent variable is \(X\) and the predictors are \(X\) along with all its integer powers up to a integer \(n\), which is \(X, X^2, ...., X^n\)

Is this a Polynomial Regression calculator with steps?

Steps are shown in the sense that the involved matrices that need operation are clearly identified, and the matrix operations are clearly stated.

Showing every single algebraic step of the process in a very long matrix calculation such as the ones required in this case would not be feasible.

How do you find the polynomial regression by hand?

You could, in theory, do the calculations by hand, but in this case since many variables are involved, the calculations include matrix operations, such as inverting a matrix, which is really cumbersome to do by hand.

Other Regression calculators

Regression is one the most commonly used and versatile models in statistics, where one or more predictors are used to predict the value of a scale dependent variable Y.

When you want to use only one predictor, without power, you can use this simple linear regression calculator instead. Or if you have multiple predictors, you need to use this multiple linear regression calculator .

One of the main characteristics of the regression model is that the dependent variable is assumed to be interval. There are many cases in which we would like to estimate a model in which the dependent variable is binary (0 - 1). In those cases, we need to use a logistic regression.