# Quartic Regression Calculator

## Quartic Regression Calculator

Calculate the quartic regression equation from data points

How can you find the best curve to fit your data points? Here is our **Quartic Regression Calculator** that can help you determine the quartic equation that best fits your data. Enter your data points into the calculator to find the quartic regression equation.

### How to Use?

To use the calculator is straightforward. Here’s how:

**Data Points**: Enter your data points as pairs (e.g.,`1,2 2,4 3,6`

) into the calculator.**Calculate**: Click the “Calculate” button to find the quartic regression equation.

For example, input data points `1,2 2,4 3,6`

and then click “Calculate” to get the regression equation.

### What is Quartic Regression?

Quartic regression is a type of polynomial regression. It fits a curve to your data points using a fourth-degree polynomial. This means the equation has terms up to ${x}^{4}$.

### Quartic Regression Formula

The quartic regression equation is:

$y=a{x}^{4}+b{x}^{3}+c{x}^{2}+dx+e$

**Variables**

Variable | Description |
---|---|

$a$ | Coefficient for ${x}^{4}$ |

$b$ | Coefficient for ${x}^{3}$ |

$c$ | Coefficient for ${x}^{2}$ |

$d$ | Coefficient for $x$ |

$e$ | Constant term |

$x$ | Independent variable (input data points) |

$y$ | Dependent variable (output data points) |

### How To Calculate Quartic Regression

#### Example 1:

**Data Points**:`1,1 2,8 3,27 4,64`

**Calculation Steps:**

**Input Data Points**:`1,1 2,8 3,27 4,64`

**Form the System of Equations**: Use the data points to form equations based on the quartic formula $y=a{x}^{4}+b{x}^{3}+c{x}^{2}+dx+e$**Solve for Coefficients**: Use linear algebra techniques to solve for $a,b,c,d,e$.**Result**: The quartic regression equation might look like $y=1{x}^{4}-2{x}^{3}+3{x}^{2}-4x+5$

#### Example 2:

**Data Points**:`0,1 1,0 2,3 3,8`

**Step-by-Step Calculation:**

**Input Data Points**:`0,1 1,0 2,3 3,8`

**Form the System of Equations**: Use the quartic formula to set up equations.**Solve for Coefficients**: Find the values of $a,b,c,d,e$ using the data points.**Result**: The quartic regression equation might be $y=0.5{x}^{4}-1.5{x}^{3}+2{x}^{2}-1.5x+1$.

### Final Thought

The Quartic tool fits a curve to data. It finds the best 4th degree polynomial. This equation lets you see trends and forecast better. Use your facts to get the top curve match. Test it on your own numbers and see the best bend.