Response on the vertical axis, chosen from the decision

The question decides the axes

Maple & Birch's marketing lead asks: does advertising move sales? She has six stores, last quarter's ad spend and sales for each, in thousands of dollars:

> stores
  store adspend sales channel
1     1       2    20    Mall
2     2       4    27  Street
3     3       5    31    Mall
4     4       7    38  Street
5     5       8    40    Mall
6     6      10    48  Street

Two numeric variables, and a model needs to know which is which. The response — y, the vertical axis — is the thing the decision is about: sales. The explanatory variable — x, horizontal — is the thing that might explain it and that the business can turn up or down: ad spend. The rule is not "the bigger numbers", not "the first column", and not "the one you control" on its own — it is what would change if the decision went the other way. A CFO deciding next quarter's ad budget wants to know what happens to sales; sales is y.

Get this backwards and every later number — the slope, the prediction — answers a question nobody asked.

Worked example — draw it, then read it

Module 8 chose a scatter for two numerics. In Sheets, Insert → Chart → Scatter with adspend as the first column; in R, the two vectors in x-then-y order:

> plot(stores$adspend, stores$sales, xlab = "Ad spend (k$)", ylab = "Sales (k$)")

Six points climbing from (2, 20) at the bottom left to (10, 48) at the top right. Read a scatter in a fixed order:

• Direction — positive: more ad spend goes with more sales.
• Form — linear: a straight line would pass close to every point; no curve, no bend.
• Strength — strong: the points sit tightly on that line, with little scatter around it.
• Outliers — none: no store is far from the pattern the other five make.

Strength is about tightness, not steepness. A shallow line with the points exactly on it is a strong relationship; a steep line with points scattered widely is a weak one. Lesson 13.2 gives strength a number.

The swap that makes no noise

plot(stores$sales,stores$adspend) runs without complaint — R plots whatever is first on the horizontal axis. The picture is the same six points reflected across the diagonal, and a line fitted to it predicts ad spend from sales: a real quantity, but not the one the CFO asked for. There is no error because R does not know what the decision is. You do; put x first.

Type the plot call, then assign x and y for three questions

CRISP-DM: choosing the response from the business objective is business understanding finishing its job before modelling begins.