17 POLYNOMIAL REGRESSION WITH BACKWARD ELIMINATION

17 POLYNOMIAL REGRESSION WITH BACKWARD ELIMINATION
In the 17th Minitab tutorial, we visit the Smartboard Company high-speed test track again. On this outdoor test track, which stretches downhill over several miles, the influence of the following parameters on the maximum achievable speed of a skateboard prototype is to be tested: The deck width in millimeters, the so-called deck flex as a measure of the elasticity of the skateboard decks in the two stages medium and hard, as well as the wheel hardness. The wheel hardness is determined according to the standardized Shore hardness test method. A metal pin with a geometrically standardized truncated cone tip, and a standardized spring force, and application time is pressed into the wheel surface. The greater the resistance of the skateboard wheel to the penetration of the metal pin the greater the hardness value achieved. The central aim of this Minitab tutorial is to find out which of the three influencing variables, also known as predictors, have a significant effect on our response variable – in this case the wheel hardness. To do this, we will first work with the so-called matrix plot to create a visual overview of possible trends and tendencies in advance. We will then use Pearson’s correlation factor to numerically assess the characteristics of the trends and tendencies identified, and derive our corresponding variance model using polynomial regression analysis. As part of the evaluation of our variance model based on the classic quality parameters, we will become familiar with other quality parameters in this context, such as the PRESS value, or the Mallow cp value. We will then get to know the „backward elimination“ method, which is very important for model adjustment in order to remove non-significant terms from our variance model. Finally, we will learn about the very helpful and efficient option of automated backward elimination, and the regression of the best subsets, so that we can finally use the available results to make a statement about the extent to which the respective influencing variables affect the roll hardness.

MAIN TOPICS MINITAB TUTORIAL 17

• Polynomial regression with backward elimination
• Correlation matrix
• Editing the correlation matrix
• Correlation analysis according to Pearson
• Table of „pairwise correlations“
• Analysis of the residual scatter
• Automated backward elimination
• Table Regression of the best subsets
• Quality parameters PRESS, Mallows-Cp, AICc, BIC