 ## de.lmu.ifi.dbs.elki.math.statistics Class PolynomialRegression

```java.lang.Object de.lmu.ifi.dbs.elki.math.statistics.MultipleLinearRegression de.lmu.ifi.dbs.elki.math.statistics.PolynomialRegression
```

`public class PolynomialRegressionextends MultipleLinearRegression` A polynomial fit is a specific type of multiple regression. The simple regression model (a first-order polynomial) can be trivially extended to higher orders.

The regression model y = b0 + b1*x + b2*x^2 + ... + bp*x^p + e is a system of polynomial equations of order p with polynomial coefficients { b0 ... bp}. The model can be expressed using data matrix x, target vector y and parameter vector ?. The ith row of X and Y will contain the x and y value for the ith data sample.

The variables will be transformed in the following way: x => x1, ..., x^p => xp Then the model can be written as a multiple linear equation model: y = b0 + b1*x1 + b2*x2 + ... + bp*xp + e

Field Summary
` int` `p`
The order of the polynom.

Constructor Summary
```PolynomialRegression(Vector y, Vector x, int p)```
Provides a new polynomial regression model with the specified parameters.

Method Summary
` double` `adaptedCoefficientOfDetermination()`
Returns the adapted coefficient of determination
` double` `estimateY(double x)`
Performs an estimation of y on the specified x value.
`private static Matrix` ```xMatrix(Vector x, int p)```

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.MultipleLinearRegression
`coefficientOfDetermination, estimateY, getEstimatedCoefficients, getEstimatedResiduals, getSumOfSquareResiduals, getSumOfSquaresTotal, getVariance, toString`

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Field Detail

### p

`public final int p`
The order of the polynom.

Constructor Detail

### PolynomialRegression

```public PolynomialRegression(Vector y,
Vector x,
int p)```
Provides a new polynomial regression model with the specified parameters.

Parameters:
`y` - the (n x 1) - vector holding the response values (y1, ..., yn)^T.
`x` - the (n x 1)-vector holding the x-values (x1, ..., xn)^T.
`p` - the order of the polynom.
Method Detail

### xMatrix

```private static Matrix xMatrix(Vector x,
int p)```

`public double adaptedCoefficientOfDetermination()`
Returns the adapted coefficient of determination

Returns:
`public double estimateY(double x)`
`x` - the x-value for which y is estimated