Q 499. Interaction effect is the combined effect of 2 or more factors on the response variable. Both Multiple Linear Regression (MLR) and Design of Experiments (DOE) can provide information on such interaction effects. Why is it that we get better information about the interaction effects from the output of DOE analysis? 

 

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

• All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/
• Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. Questions launched on Tuesdays are open till Friday and questions launched on Friday are open till Tuesday. 
• When you respond to this question, your answer will not be visible till it is reviewed. Only non-plagiarised (plagiarism below 5-10%) responses will be approved. If you have doubts about plagiarism, please check your answer with a plagiarism checker tool like https://smallseotools.com/plagiarism-checker/ before submitting. 
• The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

Multiple Linear Regression (MLR) 

 

Multiple linear regression is the most common form of linear regression analysis As a predictive analysis, the multiple linear regression is used to explain the relationship between one continuous dependent variable and two or more independent variables. The independent variables can be continuous or categorical (coded appropriately). 

The Variable that we want to predict is known as the dependent variable and variables we use to predict the value of the dependent variable are known as independent variables. 

 

                                                         Multiple linear regression model predictions graph 

 

Multiple linear regression can give predictions in 2 forms- Linear regression and non-linear regression. 

If we refer the above regression equation; MLR give us the information of main effects of independent variables only. 

 

Design of Experiment (DOE) 

Below is the experiments results from 3 factors - 2 level full factorial DOE. 

Speed, quality and service are the factors and Satisfaction is the outcome/ response. 

Lets analyze this data with the help of Minitab to know about main and interaction effects. 

 

 

 

R- Adjusted value 99.03% shows that this model is very much fitted and very accurate for regression analysis. 

 

Above data shows that Speed has most significant impact on response, then Quality and then service followed by Quality-service (Interaction effects) on response. 

 

Above Regression equation shows all main and interaction effects on response as - satisfaction. 

 

 

Alias structure shows we have single, 2 way and 3 way interaction effects in this case. 

 

 

We can clearly see the main and interaction effects among all the factors or variables. And insignificant interaction effects could be removed from the Regression equation for better understanding of situation or Project study. 

 

Regression equation and Pareto chart after model reduction (Elimination of non significant effects from the model) 

 

 

Conclusion: 

DOE analysis gives us the better information related to interaction effects as compare to Multiple Linear Regression (MLR)  

MLR uses happenstance data gathered, in this case, there is no guarantee historical data contains all the factors in which we are interested. We might miss some factors. It is also possible we want to check to look at three variable interactions but data have only two-level interactions. Happenstance data may contain some noise factors.

if happenstance data contain a noise factor it can mislead the interaction factor, we cannot get better information about the interaction effect.

DOE – If we are creating experimental data we can control the variable and check the interaction between variable factors by controlling all noise factors. This will give us a correct and authentic interaction effect. By choosing DOE will give a clear-cut interaction effect.

With DOE you can do blocking & noise treatments to ensure signals comes from the factors. 

With DOE we would have more control & accurate measurement system compared to MLR.

Both Multiple Linear Regression (MLR) & Design of Experiments (DOE) provide appropriate information on the interaction effects, however when we compare the two DOE has an edge when it comes to extracting information about the interaction effects. Below are some reasons that can be thought of which can support the above assertion:-

 

• In Design of Experiments, the experimental conditions are controlled by the experimenter. On the other hand regression analysis is done mostly on observational data which might not come from a controlled environment.

 

• There are elements of bias when it comes to observational data i.e. let’s say if we collect data on height of students in a primary school, the data will be collected from all students regardless of the gender & this can result in bias in the results. However when we are performing experiments we can select an even proportion of boys & girls in our sample in order to eliminate or reduce this bias.

 

• Although Regression models can easily explain effect of variables on the target variable i.e. both main & interaction effects, there is still a random error component that is present in all regression models thus making it difficult to understand the sources of variation which is not the case with DOE where we are carefully designing the structure of the experiment & the results will give a more comprehensive view of the sources of variation.

 

• In a Regression study as well as in DOE , we can check for the effect of interaction effects through interaction plots however we can go a step further in DOE & find out the optimal settings so as to optimize the target variable.

 

• In DOE analysis, we can also look into the impact of both main as well as interaction terms on the target variable through Pareto & can take a conscious decision in terms of variable selection basis their sensitivity on the output.

 

When the influence of one variable is dependent on the value of another variable, this is referred to as an interaction effect. DOE, Regression models, and ANOVA all have interaction effects.

 

Many variables can influence the outcome of any study, whether it's a taste test or a manufacturing process. Changing these variables can have a direct impact on the outcome. Changing the meal ingredient in a tasting test, for example, might impact overall satisfaction. This type of impact is known as a main effect. While assessing just key impacts is very simple, it is possible to make a mistake.

 

The independent variables may interact with one other. Interaction effects show that a third variable alters the connection between two variables. Statistically, these variables interact in this case because the connection between an independent and dependent variable varies based on the value of a third variable. For example, the link between ingredient and enjoyment is likely to vary depending on the type of cuisine.

 

 

The parallel lines in the interaction graphic above suggest that some of the interactions are not significant. Interaction is demonstrated by lines that are not parallel or crossed.

 

Understanding the interaction of your factors will give you a better understanding of the link between your factors and response variables. Understanding how interactions operate will allow you to improve your process more effectively than simply knowing the major effects of your elements.

Most statistical software will produce a p-value or other statistical measure of the significance of your interactions. While an interaction plot is straightforward to grasp, you should not make conclusions until you have completed the statistical analysis.

 

Changes in your response variable can be ascribed to either the influence of individual variables or the effect of factor interactions. The interaction effects are what differentiates a regression analysis from a DOE. Regression does not make it easier to determine interaction.

 

Consider potential interactions while deciding which components to include in your DOE. Your DOE results will either validate or refute your assumptions.

 

In DOE, an interaction occurs when the influence of one factor on a response variable is affected by the level or settings of another component. An interaction plot is the simplest technique to determine whether or not there are any two-way interactions. There is no interaction if the lines are parallel. There is a significant possibility of interactions if the lines cross or are not parallel. This must be statistically proved, not just aesthetically. Furthermore, depending on the amount of components, you might have many interactions.

 

You will discover two types of effects or impacts that your variables will have on your response variable as a consequence of doing a DOE. One is the influence of a single element on the reaction on its own. This is known as a main effect. The other type of impact is an interaction effect, which is the influence of one element on the settings or levels of another component. An interaction plot depicts the consequences of interactions. This is made up of a sequence of lines that depict the variables and the reaction. There is no interaction between the elements if the lines are parallel. If the components are crossed or non-parallel, as proven by statistical analysis, there is an interaction between them.

Ambikesh Tiwari has given the correct answer to this tricky question. Well done!