Correlation and linear regression

Use the chemical-and-bacteria data in Review 2. Fit y on x and then x on y. Draw the residuals in the response direction for each fit: vertical for y on x, horizontal for x on y. Explain why each line minimises a different sum of squared discrepancies, so rearranging one fitted equation generally does not produce the other.

For the comparison requested in the question, refit without the suspect observation and inspect both the scatter and correlation again. In an investigation, excluding an observation needs a reason beyond improving the coefficient. Explain why correlation alone cannot establish a suitable model or a causal explanation, and check whether a proposed prediction stays inside the observed range.