Linear Model Building

Linear Model Building

In the previous lesson, we talked about Planning Experiments. Let's move forward.

Here is the key question: How do we analyze experimental data quickly and effectively? How do we develop a generalized approach that works for most of our product development and process improvement problems?

The answer: Build Linear Models.

Albert Einstein, said:

Make things as simple as you can, but no simpler.

Linear models are simple and smart.

A linear model is a very good general purpose powerful, yet simple solution:

A linear model is a good solution because:

It is simple - it has fewer parameters.

It is easy to build.

It is easy to use.

It is scalable; it can be applied to small problems involving a few variables; or, it can be easily applied to BIG problems with a large number of variables.

It is easy to understand.

It is theoretically sound.

It has predictive power.

It provides us with x-ray vision.

So how do we build linear models?

I have good news for you, the lab R&D Scientist.

Now you have an able R&D lab assistant, FReD the bot. Fred will make your job an order of magnitude easier. He will analyze all your lab R&D data automatically. 

Here is what FReD, the bot, will do for you: Our Cheesecake example has 8 Controls - recipe and process variables and 6 Responses.

  1. 1
    Calculate corrlelations between all Control and Response Variables and summarize them in a nice Correlation plot.
  2. 2
    Show 8 x 6 = 48 Scatter Plots.
  3. 3
    Show 8 x 6 = 48 Scatter plots with Model trends.
  4. 4
    Summarize Linear models for six responses in 6 x 3 = 18 tables
  5. 5
    Generate 6 + 1 = 7 Optimums for various interesting scenarios.
  6. 6
    Generate 6 + 1 = 7 possible interesting new product/process ideas 
  7. 7
    Generate 3 tables for possible Quality Control Use
  8. 8
    And summarize all the above information in a standardized, easy to read, easy to share and easy to publish technical report. Hopefully eliminating 40-80 hours of technical drudgery for each report you need to generate.

And now, all you have to do is interpret the linear models generated by FreD the bot.

As a small sample of these, here are two graphics. 

In the middle of this Correlation plot, you see a number -0.8 over a light red circle that points to "Bake Temp(Baking Temperature)" on left hand side and "Moisture" on the bottom. This relationship conveys that "Higher the Baking Temperature, lower the Moisture."

There is a ton of information compactly stored in this diagram.

Here is another example. The above scatter plots and Model Trends diagram compactly stores 8 x 6 = 48 scatter plots. If you see a small scatter plot on the upper right hand corner, it shows the scatter plot of Baking Temperature versus Moisture. The graph shows higher the Baking Temperature, Lower the Moisture. There are 48 such relationships displayed in diagram above.

The above two examples are a small sample of all the information you can glean from your R&D project.

You get the idea of the power of FReD, the bot's Linear Model Builder.

This concludes this short lesson, Lesson 5: Linear Model Builder. 

Next is Lesson 6: Optimize for Product/Process Performance.

About Author

Mukul Mehta

Mukul Mehta has over 40 years of proven industrial experience in chemical , polymer, and plastics industry. Worked as a Sr. Manager, Statistics and Computer Aided Research for BF Goodrich Chemical, a Fortune 500 company, and then as a software entrepreneur, promoted "quantitative, predictive modeling in one minute or less as a mantra for R&D and New Product Development." Many multi-million dollar successes for dozens of Corporate R&D clients in chemical and pharma industry. Trained over 750 R&D chemists, engineers and managers to Speedup New Product Development through statistical design of experiments.

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