Scatterplots

A table of numbers hides patterns because your eye can't scan two columns at once and judge a trend. A scatterplot fixes that by turning each pair of values into a single point in a plane. Once every individual is a dot, your eye does the statistics for free: you can see whether the dots climb, fall, curve, or scatter randomly, and whether they hug a tight line or spread out loosely. That visual read is the first and most important step in any regression analysis, before you compute a single number.

Building one is mechanical. Pick the explanatory variable, the one you think helps predict or explain the other, for the x-axis, and the response variable for the y-axis. Scale each axis to fit its own variable's range, then plot one point per individual. For 20 cars, weight (in pounds) goes on x and fuel economy (in miles per gallon) goes on y; each car contributes one dot, and the finished cloud of 20 points typically drifts downward, heavier cars getting fewer miles per gallon. For the pairs (1,3), (2,5), (3,4), (4,8), (5,9), (6,11), plotting x from 1 to 6 against y shows a rough upward drift with a little scatter around it.

Axes are not interchangeable. Putting hours studied on y instead of x doesn't change the pattern's strength or form, since you're plotting the same pairs, but it flips which variable is being explained by which, and that changes how you'd describe the relationship in words. A scatterplot also extends naturally: color-coding a third, categorical variable lets you check whether the x-y relationship holds the same way inside every subgroup, which sets up later questions about lurking variables and whether one line really fits everyone.