Orthogonal Polynomials in MINITAB

Synthetic Fiber Example

Setup

Assume the data already entered in C1 (strength) and C2 (cotton). To create linear column do DataCodeNumeric to numeric

(fiber01.png here)
Do likewise for quadratic, cubic, and quadratic.

Run Regression

Do RegressionRegression

(fiber02.png here)

Session Output

Regression Analysis: strength versus linear, quadratic, cubic, quartic 

The regression equation is
strength = 15.0 + 0.820 linear − 2.21 quadratic − 1.14 cubic
                − 0.311 quartic


                                         
Predictor     Coef  SE Coef      T      P
Constant   15.0400   0.5678  26.49  0.000
linear      0.8200   0.4015   2.04  0.055
quadratic  −2.2143   0.3393  −6.53  0.000 **
cubic      −1.1400   0.4015  −2.84  0.010 *
quartic    −0.3114   0.1518  −2.05  0.053


S = 2.83901   R-Sq = 74.7%   R-Sq(adj) = 69.6%


Analysis of Variance

                                                
Source          DF      SS      MS      F      P
Regression       4  475.76  118.94  14.76  0.000
Residual Error  20  161.20    8.06              
Total           24  636.96                      


                     
Source     DF  Seq SS
linear      1   33.62    C1
quadratic   1  343.21    C2
cubic       1   64.98    C3
quartic     1   33.95    C4