**16 POLYNOMIAL REGRESSION
**In the 16th Minitab tutorial, we are once again in the heat treatment department at Smartboard Company. Due to the current high order situation, the heat treatment plant is currently a bottleneck unit, and the quality team should therefore investigate whether it is possible to achieve the axle strength previously required by customers even with reduced annealing times by increasing the annealing temperature. By increasing the annealing temperature, the annealing times of the skateboard axles in the heat treatment plant could be shortened, so that more axles can be heat treated faster. In this Minitab course, we will first determine the corresponding Pearson correlation factors using a simple correlation analysis. Based on these findings, we will apply the useful so-called polynomial regression analysis, to mathematically model the reciprocal relationships between influencing variables and the response variable. Starting from a linear model, we will first generate a quadratic, and then a cubic model, and compare them with each other. Using the corresponding residual diagrams, we will examine why a cubic regression equation is preferable to a linear or quadratic regression equation in this training unit. Finally, we will enter into the very useful interactive response variable optimization, and with our previously determined regression equation, we will be able to determine the required best possible parameter settings with a 95% certainty within the framework of the response variable optimization.

MAIN TOPICS MINITAB TUTORIAL 16

- Polynomial regression
- Correlation analysis
- Correlation matrix
- Table of „pairwise correlations“
- Hypothesis test as part of the pairwise correlation analysis according to Pearson
- Reference lines in the matrix plot
- Polynomial regression
- „4 in 1“ – residual diagram
- Quadratic and cubic regression models
- Response variable optimization in the context of regression analysis
- Confidence and prediction intervals in the context of the regression analysis