Tabtrainer® Series - Correlation and Regression in Minitab®

Explore the curriculum of Simple Correlation and Regression.

In this training unit, participants are introduced to a real-world business case from the Smartboard Company, which supplies high-strength skateboard axles to Olympic teams. Due to strict strength requirements and high copper costs, the company must minimize copper content without compromising quality. Participants learn how to use correlation analysis to explore the relationship between copper content and material strength, and regression analysis to predict the optimal copper level needed to achieve 280 MPa – supporting data-driven decisions in a cost-sensitive production environment.

In this part of the training, participants begin by importing a historical data set titled "copper content", gathered by the quality team during continuous process monitoring. The dataset contains 30 entries with three columns: alloy ID, copper content (%), and achieved material strength (MPa). The goal is to explore whether there is a linear relationship between copper content and material strength using a simple correlation analysis. Since both variables are continuously scaled, they meet the requirement for such analysis. Participants are introduced to the Pearson correlation coefficient (R), which quantifies the strength and direction of a linear relationship, ranging from -1 (perfect negative) to +1 (perfect positive). A value of 0 indicates no linear correlation. Practical examples illustrate what different correlation values mean in a real production context.

In this training unit, participants perform a Pearson correlation analysis to quantify the linear relationship between copper content and material strength based on historical test data. Using statistical software, the strength is plotted on the x-axis and copper content on the y-axis. The correlation factor (R = 0.991) indicates a strong positive linear relationship, confirmed by a significant p-value (< 0.05) and a 95% confidence interval (0.981–0.996). However, no data points exist near the target strength of 280 MPa, creating a data-free zone in the critical decision area.

To address this, participants are introduced to simple linear regression. Unlike correlation, regression allows predicting unknown values and modeling cause-effect relationships. The regression function derived from the data enables calculating the required copper content for any given strength, including the unmeasured target of 280 MPa. This equips participants with a powerful tool to make data-driven decisions even in the absence of direct measurements, highlighting the practical value of regression in cost-sensitive technical environments.

In this training unit, participants will:

• Understand the concept of linear regression and its importance for predicting technical outcomes.

• Learn the structure of a regression function (y = a + b·x) and the meaning of its parameters.

• Recognize why it is not possible to fit a line perfectly through all data points and how deviations (errors) arise.

• Explore the method of least squares as a robust mathematical approach to:

  • Minimize the total squared deviations between observed and predicted values,

  • And thus find the best-fitting regression line.

• Apply these principles to a real-world problem: determining the required copper content to achieve a target material strength of 280 MPa, even in a data-free range.

This gives them the skills to translate data into predictive models, make informed business decisions, and understand the statistical foundation behind tools used in Six Sigma projects.

By the end of this training segment, participants will be able to:

• Understand the mathematical basis of the method of least squares as the standard procedure to derive a linear regression function.

• Apply basic curve sketching principles to minimize the sum of squared deviations between actual and predicted values.

• Use the chain rule to derive a function with two parameters (a and b), set up a system of equations, and solve it using basic linear algebra.

• Calculate necessary summation terms (∑x, ∑y, ∑x², ∑xy) based on actual measurement data.

• Derive the final regression function i

• Use the regression function to predict unknown values.

• Recognize how this mathematical approach enables decision-making in areas with no measured data – a key element in Six Sigma projects and predictive quality control.

By the end of this section, participants will be able to:

• Perform a regression analysis in Minitab using the "Fitted Line Plot" function.

• Set up the regression with copper content as the response and material strength as the predictor.

• Interpret the resulting regression function and confirm that it matches the manually derived formula.

• Understand the meaning and relevance of R-squared and adjusted R-squared values in assessing model quality.

• Use the p-value from the ANOVA table to test the statistical significance of the regression model.

• Draw conclusions about the strength and reliability of the linear relationship between copper content and strength, based on real process data from the Smartboard Company.

• Recognize that over 98% of the total data variation can be explained by the regression model, confirming its practical relevance.

• Apply these insights to make confident predictions and optimize process parameters using statistical evidence.

By the end of this section, participants will be able to:

• Generate and interpret a Four-in-One Residual Plot in Minitab to evaluate the quality of a regression model.

• Use the probability plot and corresponding p-value to assess whether the residuals follow a normal distribution (p > 0.05).

• Visually confirm normality trends through the histogram and understand its role in validating model assumptions.

• Analyze the residuals versus fits and residuals versus order plots to detect any undesirable patterns such as non-randomness or time-related trends.

• Confirm that the residuals are randomly and evenly distributed, indicating that the regression model is valid and unbiased.

• Strengthen their understanding of model diagnostics, supporting reliable interpretation and prediction in applied Six Sigma projects.

By the end of this section, participants will be able to:

• Use Minitab to activate and display confidence and prediction intervals within a regression scatterplot.

• Understand the confidence interval (inner green dotted lines) as the range within which the mean copper content of the population is expected to lie for a given strength value, with 95% certainty.

• Interpret the prediction interval (outer purple dotted lines) as the range in which a future individual copper content value will fall, for example when producing a new axle with 280 MPa, again with 95% probability.

• Recognize that the prediction interval is wider than the confidence interval, due to the natural variability of individual values compared to the mean.

• Apply this knowledge to differentiate between population-level estimates and individual predictions, which is essential for risk-aware process planning and reliable forecasting in Six Sigma projects.

• Use Minitab to perform a regression-based prediction for a target value of the predictor variable

• Interpret the predicted value of the response variable and understand its significance in process planning.

• Understand the difference between:

  • The confidence interval  and the prediction interval.

• Visually interpret both intervals in the regression scatterplot, using confidence and prediction boundaries.

• Translate statistical results into concrete business recommendations.

• Understand the practical application of regression outputs for decision-making and risk mitigation in industrial production settings.

This final chapter is dedicated to the summary of the most important findings.

Participants will learn to analyze and interpret strong correlations using matrix plots and Pearson coefficients to identify redundancies in test pilot speed profiles.