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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.

  
   

Blowing Hot Air
Hy Sedrate attempts to explain regression.

Michael J. Cleary, Ph.D.
mcleary@qualitydigest.com

 

In September’s column, we saw Hy Sedrate run regression analysis on the relationship between the number of defects in lab reports and the ambient air temperature of the lab. As a quality specialist for St. Recover in the Long Run Hospital, he had set out to decrease the defect rate, and he wanted to test his theory about the temperature. His scatter diagram showed a clear relationship between the two factors, but even more important, he learned what regression analysis actually is.

Sedrate is not known for his depth of analysis but rather for his showy style. A fast talker, he’s able to persuade those around him that he knows what he’s talking about even when he’s dead wrong. The scatter diagram that he stumbled onto to show the relationship between defects and temperature had wowed his superiors. Based on Sedrate’s chart, they invested in new air conditioning for the lab--just in time for the summer humidity that the lab workers hated. Those who benefited from the enhanced atmosphere felt that they owed it all to Sedrate and his chart.

With this success under his belt, he prepares an elaborate PowerPoint presentation in the interest of explaining regression to his peers and proving himself an expert in statistics. Sedrate displays the equation used to calculate a regression line:

His audience is truly impressed with the presentation, complemented by rising music in the background and fades into elements of the equations. As he’s closing, a quality specialist, Hap N. Stance, asks the meaning of the coefficient of determination of 0.87. Sedrate has no idea, but he reviews the PowerPoint slides once again for the benefit of his audience, which is becoming smaller with each repeated slide. Finally, he says with his usual air of confidence, “The 0.87 coefficient means that there is little determination between the two variables.”

Is Sedrate correct?

As usual, Sedrate is incorrect.

He has missed an opportunity to explain one of the few statistical tools that he could articulate in words. The coefficient of determination is the percent of variation in (the dependent variable) that can be explained by (the independent variable). Thus, if the coefficient of variation is 1.0, all the variability in y could be explained by x. A diagram that is used in many textbooks can be an aid in visualizing this concept:

As the diagram shows, the regression line explains some of the variability of ,
but not all. In Sedrate’s case, the coefficient of determination is 0.87. He should have informed his audience that 87 percent of the variability of defects can be explained by the temperature, rather than simply insinuating that temperature totally explains defect rate.

About the author

Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc., is a professor emeritus of management science at Wright State University in Dayton, Ohio. He’s the author of several articles on quality management and statistical process control. Letters to the editor regarding this column can be sent to letters@qualitydigest.com.