# Linear predictor function

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable.wikipedia

53 Related Articles

### Perceptron

**Perceptronsperceptron algorithmFeedforward Neural Network (Perceptron)**

However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis ), as well as in various other models, such as principal component analysis and factor analysis.

It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.

### Linear regression

**regression coefficientmultiple linear regressionregression**

This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. where is a disturbance term or error variable — an unobserved random variable that adds noise to the linear relationship between the dependent variable and predictor function.

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data.

### Logistic regression

**logit modellogisticlogistic model**

However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis ), as well as in various other models, such as principal component analysis and factor analysis.

The basic idea of logistic regression is to use the mechanism already developed for linear regression by modeling the probability p i using a linear predictor function, i.e. a linear combination of the explanatory variables and a set of regression coefficients that are specific to the model at hand but the same for all trials.

### Linear model

**linear modelslinearlinear process**

*Linear model

### Statistics

**statisticalstatistical analysisstatistician**

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable.

### Machine learning

**machine-learninglearningstatistical learning**

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable.

### Linear function

**linearlinear factorlinear functions**

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable.

### Linear combination

**linear combinationslinearly combined(finite) left ''R''-linear combinations**

### Linear classifier

**linearLDClinear classification**

However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis ), as well as in various other models, such as principal component analysis and factor analysis.

### Support-vector machine

**support vector machinesupport vector machinesSVM**

### Linear discriminant analysis

**discriminant analysisDiscriminant function analysisFisher's linear discriminant**

### Principal component analysis

**principal components analysisPCAprincipal components**

### Factor analysis

**factorfactorsfactor analyses**

### Y-intercept

**intercepty''-interceptintercepts**

### Dot product

**scalar productdotinner product**

using the notation for a dot product between two vectors.

### Transpose

**matrix transposetranspositionmatrix transposition**

where and are assumed to be a (p+1)-by-1 column vectors, is the matrix transpose of (so is a 1-by-(p+1) row vector), and indicates matrix multiplication between the 1-by-(p+1) row vector and the (p+1)-by-1 column vector, producing a 1-by-1 matrix that is taken to be a scalar.

### Row and column vectors

**column vectorrow vectorvector**

where and are assumed to be a (p+1)-by-1 column vectors, is the matrix transpose of (so is a 1-by-(p+1) row vector), and indicates matrix multiplication between the 1-by-(p+1) row vector and the (p+1)-by-1 column vector, producing a 1-by-1 matrix that is taken to be a scalar.

### Matrix multiplication

**matrix productmultiplicationproduct**

where and are assumed to be a (p+1)-by-1 column vectors, is the matrix transpose of (so is a 1-by-(p+1) row vector), and indicates matrix multiplication between the 1-by-(p+1) row vector and the (p+1)-by-1 column vector, producing a 1-by-1 matrix that is taken to be a scalar.

### Scalar (mathematics)

**scalarscalarsbase field**

### Random variable

**random variablesrandom variationrandom**

where is a disturbance term or error variable — an unobserved random variable that adds noise to the linear relationship between the dependent variable and predictor function.

### Design matrix

**data matrixdesign matricesdata matrices**

The matrix X is known as the design matrix and encodes all known information about the independent variables.

### Dependent and independent variables

**dependent variableindependent variableexplanatory variable**

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable. The matrix X is known as the design matrix and encodes all known information about the independent variables.

### Least squares

**least-squaresmethod of least squaresleast squares method**

This makes it possible to find optimal coefficients through the method of least squares using simple matrix operations.

### Moore–Penrose inverse

**Moore–Penrose pseudoinverseMoore-Penrose pseudoinversepseudoinverse**

The matrix is known as the Moore-Penrose pseudoinverse of X.

### Invertible matrix

**invertibleinversenonsingular**

The use of the matrix inverse in this formula requires that X is of full rank, i.e. there is not perfect multicollinearity among different explanatory variables (i.e. no explanatory variable can be perfectly predicted from the others).