Regression

From Wikipedia:

In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Note: It is still in active development, so the API may still shift, but it is also finally in a usable state for probably most use cases. Use, but with caution.

Installation

Add this line to your composer.json file and update:

"mcordingley/regression": "~0.9.2"

That's it!

Quick Start

For basic usage, add a use statement to import SimpleRegression into your current namespace:

use mcordingley\Regression\SimpleRegression;

Then instantiate a new instance of this and add data to it:

$regression = new SimpleRegression;

$regression->addData(2, [3, 5, 7, 2, 8, 10])
           ->addData(4, [3, 2, 1, 5, 5, 9])
           ->addData(6, [1, 2, 3, 4, 5, 6])
           ->addData(8, [1, 3, 4, 7, 7, 12])
           ->addData(10, [19, 17, 15, 14, 5, 1]);

The first argument to addData is the observed outcome. The second is an array of explanatory data associated with that outcome. If performing a single regression instead of a multiple regression, just supply a single value to the array.

After you're done adding data, you can get the intercept, the coefficients on the explanatory data, and the R-squared value that shows how well the fitted trend line matches the data:

$intercept = $regression->getIntercept();
$coefficients = $regression->getCoefficients();
$rSquared = $regression->getRSquared();
$seCoefficients = $regression->getStandardErrorCoefficients();
$tValues = $regression->getTValues();

You can also use the regression to predict values based on a new or hypothetical set of explanatory data:

$predictedOutcome = $regression->predict([1, 2, 3, 4, 5, 6]);

Advanced Use

SimpleRegression is a facade (in the GoF sense) over the other classes in this library. To make use of the more advanced features in this library, you'll need to get your hands dirty with the constituent classes.

Start by instantiating an instance of Regression:

use mcordingley\Regression\Regression;

$regression = new Regression;

By default, the regression uses the Linear Least Squares method of estimating the regression coefficients. If you have some alternate method that you would like to use, pass an instance of your own class that implements mcordingley\Regression\RegressionAlgorithm\RegressionAlgorithmInterface into the Regression constructor as its only argument. If you think your new algorithm would be of general use to others, please submit it in a pull request.

Next, apply any transformation logic to your data if data that you are using is non-linear. This is done by injecting objects that implement the mcordingley\Regression\Linking\LinkingInterface interface into the following methods:

$regression->setDependentLinking($linking); // To transform Y values
$regression->setIndependentLinking($linking); // To transform X values regardless of position in the data
$regression->setIndependentLinking($linking, $index); // To transform the X values that are at $index position in the data in preference to the linking set above

Currently, these linking objects ship with the library:

• mcordingley\Regression\Linking\Identity: Passes data through untransformed. Used by default unless something else is specified.
• mcordingley\Regression\Linking\Power: For data that follows a geometric progression. Constructor takes the exponent as its argument. Default 2.
• mcordingley\Regression\Linking\Exponential: For data that follows an exponential progression. Constructor takes the base of the exponent as its argument. Default M_E.
• mcordingley\Regression\Linking\Logarithm: For data that follows a logarithmic progression. Constructor takes the base of the logarithm as its argument. Default M_E.

Depending on your data, other transformations may be appropriate. If you end up developing a transform for use with your data that is not included already here and that you think would be of use to others, please submit it in a pull request.

Adding data and pulling out the coefficients is also slightly different than with the SimpleRegression object. The idea of an intercept is an abstraction that is introduced by that object. When dealing with the data and computed coefficients, you have to introduce a constant 1 as your first data point. This represents the idea of invariance as a predictive "variable". Your first computed coefficient is therefore your intercept. If this is still confusing, take a look at the implementation of SimpleRegression to see how it abstracts this out for you. The base Regression class leaves altering this up to you, so you have the freedom to deviate from how SimpleRegression implements this if necessary.

$regression->addData(2, [1, 3, 5, 7, 2, 8, 10])
           ->addData(4, [1, 3, 2, 1, 5, 5, 9])
           ->addData(6, [1, 1, 2, 3, 4, 5, 6])
           ->addData(8, [1, 1, 3, 4, 7, 7, 12])
           ->addData(10, [1, 19, 17, 15, 14, 5, 1]);

As such, the Regression class does not have the getIntercept method that SimpleRegression has. Otherwise the remaining methods operate the same, albeit without stripping off the first value from array return values:

$coefficients = $regression->getCoefficients();
$rSquared = $regression->getRSquared();
$seCoefficients = $regression->getStandardErrorCoefficients();
$tValues = $regression->getTValues();
$predictedOutcome = $regression->predict([1, 1, 2, 3, 4, 5, 6]); // Note added 1 at the start

Prerequisites For 1.0

• Get more tests in place. An adventurous early adopter of this library could run real-world data through an external tool to generate test values to put into unit tests here.