LinearRegression (Morphokinetics)

java.lang.Object
- utils.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.

Author:

Robert Sedgewick, Kevin Wayne

Field Summary

Fields
Modifier and Type Field and Description

private double intercept

private double r2

private double slope

private double svar0

private double svar1

Fields
Modifier and Type	Field and Description
`private double`	`intercept`
`private double`	`r2`
`private double`	`slope`
`private double`	`svar0`
`private double`	`svar1`

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

All Methods Instance Methods Concrete 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

- Field Detail
  - intercept
```
private final double intercept
```
  - slope
```
private final double slope
```
  - r2
```
private final double r2
```
  - svar0
```
private final double svar0
```
  - svar1
```
private final double svar1
```
- 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

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

intercept

slope

r2

svar0

svar1

Constructor Detail

LinearRegression

Method Detail

intercept

slope

R2

interceptStdErr

slopeStdErr

predict

toString