LinearRegression

java.lang.Object
- LinearRegression

```
public class LinearRegression
extends java.lang.Object
```
The LinearRegression class performs a simple linear regression on an set of N data points (y_i, x_i). That is, it fits a straight line y = α + β x, (where y is the response variable, x is the predictor variable, α is the y-intercept, and β is the slope) that minimizes the sum of squared residuals of the linear regression model. It also computes associated statistics, including the coefficient of determination R² and the standard deviation of the estimates for the slope and y-intercept.

Constructor Summary

Constructors
Constructor and Description

LinearRegression(double[] x, double[] y)
Performs a linear regression on the data points (y[i], x[i]).

Constructors
Constructor and Description
`LinearRegression(double[] x, double[] y)` Performs a linear regression on the data points `(y[i], x[i])`.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`intercept()` Returns the y-intercept α of the best of the best-fit line y = α + β x.
`double`	`interceptStdErr()` Returns the standard error of the estimate for the intercept.
`double`	`predict(double x)` Returns the expected response `y` given the value of the predictor variable `x`.
`double`	`R2()` Returns the coefficient of determination R².
`double`	`slope()` Returns the slope β of the best of the best-fit line y = α + β x.
`double`	`slopeStdErr()` Returns the standard error of the estimate for the slope.
`java.lang.String`	`toString()` Returns a string representation of the simple linear regression model.

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

- Constructor Detail
  - LinearRegression
```
public LinearRegression(double[] x,
                double[] y)
```
    Performs a linear regression on the data points (y[i], x[i]).
    
    Parameters:
    x - the values of the predictor variable
    y - the corresponding values of the response variable
    
    Throws:
    
    java.lang.IllegalArgumentException - if the lengths of the two arrays are not equal
- Method Detail
  - intercept
```
public double intercept()
```
    Returns the y-intercept α of the best of the best-fit line y = α + β x.
    
    Returns:
    the y-intercept α of the best-fit line y = α + β x
  - slope
```
public double slope()
```
    Returns the slope β of the best of the best-fit line y = α + β x.
    
    Returns:
    the slope β of the best-fit line y = α + β x
  - R2
```
public double R2()
```
    Returns the coefficient of determination R².
    
    Returns:
    the coefficient of determination R², which is a real number between 0 and 1
  - interceptStdErr
```
public double interceptStdErr()
```
    Returns the standard error of the estimate for the intercept.
    
    Returns:
    the standard error of the estimate for the intercept
  - slopeStdErr
```
public double slopeStdErr()
```
    Returns the standard error of the estimate for the slope.
    
    Returns:
    the standard error of the estimate for the slope
  - predict
```
public double predict(double x)
```
    Returns the expected response y given the value of the predictor variable x.
    
    Parameters:
    x - the value of the predictor variable
    
    Returns:
    the expected response y given the value of the predictor variable x
  - toString
```
public java.lang.String toString()
```
    Returns a string representation of the simple linear regression model.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    a string representation of the simple linear regression model, including the best-fit line and the coefficient of determination R²

Class LinearRegression

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LinearRegression

Method Detail

intercept

slope

R2

interceptStdErr

slopeStdErr

predict

toString