A moderate correlation, and what it is not

temp_c and vibration_mm_s on sensor-telemetry move together — moderately, and positively. r = 0.62 over 8,000 rows.

That is moderate and positive. Squared, it says the linear relationship accounts for 38.9% of the variance in either column. That is the number worth quoting rather than r itself: 0.62 sounds like a much stronger claim than 38.9% does.

df[["temp_c", "vibration_mm_s"]].corr(method="pearson")
# also worth running:
df[["temp_c", "vibration_mm_s"]].corr(method="spearman")

Run Spearman next to Pearson every time. They agree when the relationship is roughly linear and diverge when it is monotone but curved — and the gap between them is a free diagnostic that costs one line.

A correlation this size will get read as a mechanism. It is not one. Both columns here are generated from a shared underlying process, which is exactly the situation a confounder creates in real data: two things that move together because a third thing moves both.

Look at the scatter before quoting r. Anscombe's quartet is four datasets with identical correlation coefficients and nothing else in common, and the correlation explorer will draw this pair so you can see which case you are in.

Longer treatment in Correlation, confounding, and Simpson's paradox.