The first chart of any two-variable question
Before any coefficient, any regression, any claim: plot the pairs. A scatter plot puts one variable on each axis and a dot per pair, and it shows what numbers hide: whether the relationship is linear or curved, tight or diffuse, driven by one outlier or consistent throughout, and whether the cloud splits into groups. Every correlation horror story in textbooks (Anscombe's quartet, the dinosaur dataset) is a case of someone quoting statistics for data they never plotted.
Advertising spend (2 to 16) against weekly sales (15, 19, 26, 24, 31, 36, 35, 42): the cloud climbs steadily with a near-constant width, r = 0.975. One point, (8, 24), sags below the trend; on inspection it is the week the shop closed for two days. The plot does not just support the analysis, it improves it: that week now gets explained instead of silently bending the line.
Reading a scatter plot in order
Direction: up, down, or none. Form: straight, curved, or fan-shaped (a fan means spread grows with X, which plain regression dislikes). Strength: how closely the dots hug the form. Exceptions: points far from the pattern; check them for recording errors before anything else. Run through those four and you have extracted most of what the chart knows.
Letting one point write the conclusion. A single far-flung pair can manufacture correlation in an otherwise shapeless cloud, or destroy a real pattern. If removing one point flips your conclusion, the finding was never solid: report it with the point, and say so.
Adding the trend line
The optional trend line here is the least squares fit: the line the linear regression calculator computes. Toggle it on to judge fit by eye: the line should thread the cloud's centre along its whole length. If the cloud curves away at both ends, the honest next step is the quadratic fit, not a straighter ruler.
Frequently asked questions
Which variable goes on which axis?
The predictor or explanatory variable on the horizontal X axis, the outcome on the vertical Y axis. Time, dose and spend are typical X choices; what you hope they explain goes on Y.
What correlation does my plot show?
The tool computes Pearson's r for the same pairs. Judge agreement between the number and the picture: if they tell different stories, believe the picture and investigate.
Can a scatter plot show more than two variables?
Colour or size can encode a third (a bubble chart). Use sparingly: two well-chosen variables read clearly, five encoded ones read like weather maps.
My points form a curve. Is correlation useless?
Pearson's r understates curved relationships. Spearman's rho handles steadily climbing curves, and quadratic regression fits a one-bend curve outright. Both are linked below.