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• Chris Butterworth

# Learning Through Data - Residual Analysis

In this post I want to describe a simple technique that can lead to learning something new. In this case, we found out something interesting and useful when we looked closely at some measurement data for a new product.

The product is a power tool and our data set consists of power (input) and torque (output). As you increase power, you should see a proportional increase in torque. In this first prototype evaluation we collected a set of data that covered the range of input power. The chart below shows the scatterplot of Torque vs Power.

The chart confirms our expectations. Now, fitting a straight line to this data gives the following chart.

It looks like a good match to our data. the next step is to look at the residuals. A residual is the difference between observed and expected - the difference between the plotted data point and the fitted line. Below is a plot of the residuals for our model.

It is clear that a straight line model fit misses some structure in the data. This was also visible, but less obvious, in the fitted line plot above. A second order model (polynomial, 2) would be a better fit to this data. The next plot shows the data with this curved fit line.

Clearly this is a better fit to the data but a look at the new residuals shows that it isn't perfect.

Even though we fit a second order model to the data, a higher order model is required. In our case we aren't interested in determining the model so much as understanding how the tool performs. The behaviour at the bottom of the tool's range was due to other factors related to the test equipment.

This example was repeated on the second prototype and resulted in the same residual patterns. We learned a few things about our equipment and our product as a result of these analyses.

I ran my analysis in RStudio but you could certainly do the same in Microsoft Excel.

It is important to develop your analytical skills because data analysis often leads to new insights. I hope you find some value in this method.