Statistics Toolbox

x2fx

Transform a factor settings matrix to a design matrix

Syntax

• D = x2fx(X)
  D = x2fx(X,'model')
  

Description

D = x2fx(X) transforms a matrix of system inputs, X, to a design matrix for a linear additive model with a constant term.

D = x2fx(X,'model') allows control of the order of the regression model. 'model' can be one of these strings:

'interaction'	Includes constant, linear, and cross product terms
'quadratic'	Includes interactions and squared terms
'purequadratic'	Includes constant, linear, and squared terms

Alternatively model can be a matrix of terms. In this case, each row of model represents one term. The value in a column is the exponent to which the same column in X for that term is raised, D(i,j) = prod(x(i,:).^model(j,:)). This allows for models with polynomial terms of arbitrary order.

The order of columns for a quadratic model is:

1. Constant term
2. Linear terms (the input X columns 1,2,...,k)
3. Interaction terms formed by taking pairwise products of X columns (1,2), (1,3), ..., (1,k), (2,3), ..., (k-1,k)
4. Squared terms in the order 1,2,...,k

Other models use a subset of these terms but keep them in this order.

x2fx is a utility function for rstool, regstats, and cordexch.

Examples

Example 1.

• x = [1 2 3]'; 
  model = [0 1 2]';
  D = x2fx(x,model)
  
  D =
       1     1     1
       1     2     4
       1     3     9
  

The first column is x to the 0th power. The second column is x to the 1st power. And the last column is x squared.

Example 2.

• x = [1 2 3;4 5 6]'; 
  model = 'quadratic';
  D = x2fx(x,model)
  
  D =
       1     1     4     4     1    16
       1     2     5    10     4    25
       1     3     6    18     9    36
  

Let x₁ be the first column of x and x₂ be the second. Then the first column of D is the constant term, the second column is x₁, the third column is x₂, the fourth column is x₁x₂, the fifth column is x₁², and the last columns is x₂².

See Also
rstool, candexch, candgen, cordexch, rowexch, regstats

wishrnd

xbarplot