Statistics Toolbox

polyconf

Polynomial evaluation and confidence interval estimation

Syntax

• [Y,DELTA] = polyconf(p,X,S)
  [Y,DELTA] = polyconf(p,X,S,alpha)
  

Description

[Y,DELTA] = polyconf(p,X,S) uses the optional output S generated by polyfit to give 95% confidence intervals Y ± DELTA. This assumes the errors in the data input to polyfit are independent normal with constant variance.

[Y,DELTA] = polyconf(p,X,S,alpha) gives 100(1-alpha)% confidence intervals. For example, alpha = 0.1 yields 90% intervals.

If p is a vector whose elements are the coefficients of a polynomial in descending powers, such as those output from polyfit, then polyconf(p,X) is the value of the polynomial evaluated at X. If X is a matrix or vector, the polynomial is evaluated at each of the elements.

Examples

This example gives predictions and 90% confidence intervals for computing time for LU factorizations of square matrices with 100 to 200 columns.

• n = [100 100:20:200];
  for i = n
  A = rand(i,i);
  tic
  B = lu(A);
     t(ceil((i-80)/20)) = toc;
  end
  [p,S] = polyfit(n(2:7),t,3);
  [time,delta_t] = polyconf(p,n(2:7),S,0.1)
  time =
      0.0829    0.1476    0.2277    0.3375    0.4912    0.7032
  delta_t =
      0.0064    0.0057    0.0055    0.0055    0.0057    0.0064
  

poisstat

polyfit