Exercise 3: Why a Scatter Plot's Pattern Is Never Proof of Causation — Possible Solution ==================================================================== WHAT A SCATTER PLOT ACTUALLY SHOWS ------------------------------ Per this chapter, "a visibly upward-sloping cluster of points here would be the visual signature of a strong positive correlation — ds1-6's own Pearson coefficient close to 1." A scatter plot is a direct visualization of correlation — it shows how two variables move together across the observed data points, with an upward-sloping cluster indicating that as one variable increases, the other tends to increase as well. WHY THIS IS STILL ONLY A CORRELATION, NOT MORE ------------------------------ Per this chapter, "ds1-6's own confounding-variable warning still applies at full strength here: a clear pattern in a scatter plot is a reason to investigate, never proof of a direct causal link on its own." A scatter plot is simply a picture of the exact same numeric relationship a Pearson correlation coefficient already summarizes as a single number — it doesn't add any new kind of evidence beyond what correlation already provides, since it's a visualization of that same underlying statistic, not an independent test of causation. WHY ds1-6's CONFOUNDING-VARIABLE REASONING APPLIES UNCHANGED ------------------------------ Per ds1-6, "ice cream sales and drowning incidents correlate strongly... Neither causes the other; a third, unmeasured factor... is the real driver." That example demonstrated that a strong, real, accurately measured correlation can exist entirely without any direct causal link between the two measured variables — the same underlying limitation applies just as much to a scatter plot's own visible pattern as it did to the numeric coefficient, since a scatter plot showing quantity and revenue moving together doesn't rule out some third factor (for example, larger orders naturally requiring more items AND costing more, both driven by the size of the order itself rather than quantity directly causing revenue) explaining the pattern instead. WHY PLOTTING THE RELATIONSHIP DOESN'T CHANGE THE UNDERLYING LOGIC ------------------------------ Turning a number into a picture makes a pattern easier to notice and easier to communicate (ds1-1's own "Communicate" stage) — but it doesn't introduce any new information about WHY the pattern exists. The same logical gap that prevents a correlation coefficient alone from proving causation (the possibility of an unmeasured confounding variable) is present, unchanged, in the visual version of that exact same statistic. WHY THIS WORKS AS AN ANSWER ------------------------------ It explains that a scatter plot is a direct visualization of correlation rather than a separate, stronger kind of evidence, and applies ds1-6's own confounding-variable example to show why the same causation limitation that applies to a numeric correlation coefficient applies unchanged to its visual counterpart.