14 SIMPLE CORRELATION AND SIMPLE REGRESSION

14 SIMPLE CORRELATION AND SIMPLE REGRESSION
In the 14th Minitab tutorial, we visit the heat treatment facility at Smartboard Company. Here the skateboard axles are subjected to heat treatment, in order to achieve the material strength required by the customer. In addition to the heat treatment parameters, the copper content in the skateboard axles also has an influence on the material strength. Against this background, this Minitab tutorial will investigate the relationship between copper content and material strength, on the basis of existing historical process data. For this purpose, we will first use a simple correlation analysis in this Minitab training, to investigate whether a reciprocal relationship can be established between the amount of copper in the material, and the axle material strength. If this is the case, we will use a simple regression analysis to show which copper content is ultimately required to achieve the material strength desired by the customer. As part of our correlation analysis, we will become familiar with the important Pearson correlation factor, in order to obtain a quantitative statement, as to whether the relevant influencing factors correlate weakly, strongly, or not at all. In this context, we will learn the basic principle of correlation analysis, based on the method of least squares, in detail by actively calculating a complete correlation analysis step by step by using a simplified data set, in order to understand how the results in the output window were obtained. Finally, we can use a simple regression analysis, to describe our technical problem with a mathematical regression equation, in order to predict future material strengths, as a function of the influencing factor copper content, with a high prediction quality.

MAIN TOPICS MINITAB TUTORIAL 14

• Simple correlation analysis according to Pearson
• Correlation matrix
• Table of „pairwise correlations“
• Hypothesis test for pairwise correlation according to Pearson
• Working with „drawing tools“ in the context of the matrix plot
• Simple regression analysis
• Adjusting regression model
• Least squares method
• Interpretation of fitted line plot
• Residual analysis as part of the regression
• Confidence intervals and prediction intervals
• Predicting the response variable by using the regression model