Lesson 7 of 9
A fitted line
A regression across 2,604 US listings gives a clean slope, a clean intercept and an R-squared of 0.0097. The line exists. It explains one percent of anything.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
Who writes thisEditorial processLinkedIn (opens in a new tab)X (opens in a new tab)
In one minute
- A regression finds the straight line that minimises the squared vertical distances to the data. It always finds one.
- The slope says how much the second variable moves per unit of the first. R-squared says how much of the variation the line accounts for.
- A slope can look meaningful while the R-squared says the line describes almost nothing, and both numbers have to be quoted together.
A regression will fit a line to any two columns of numbers. It never refuses, never returns nothing, and the coefficients it produces always look like findings. The number that says whether the line is worth anything is a separate one, and it is the one that gets dropped.
Two regressions from the same market, the same day
- Net margin on gross margin: R-squared0.97%
- Return on equity on return on invested capital: R-squared54.11%
What comes out of one
Three numbers, and each answers a different question.
The slope is how much the outcome moves for a one unit move in the input. The intercept is where the line crosses at an input of zero. R-squared is the share of the variation in the outcome that the line accounts for, from 0 to 1.
The line that explains nothing
Regressing net margin on gross margin across 2,604 active US listings gives a slope of 0.1476 and an intercept of minus 12.056. Read as a sentence: a company with a gross margin ten points higher has a net margin about 1.5 points higher.
That is a plausible-sounding, publishable claim. Its R-squared is 0.0097.
The line that explains something
The same day, regressing return on equity on return on invested capital across 2,001 listings gives a slope of 0.9763 and an R-squared of 0.5411. The line accounts for 54 percent of the variation, which is a real relationship.
And, as the last lesson established, it is a relationship produced by two formulas sharing most of their inputs. A high R-squared is necessary for a line to be worth reading and it is not sufficient for the line to mean anything about the world.
Four things a fitted line cannot support
Causation. The three rivals from the last lesson all survive a regression untouched.
Extrapolation. The first line predicts a net margin of minus 12 percent at a gross margin of zero. No observation anywhere near there produced that estimate; it is the line continued past its data.
A statement about one company. A line describes a cloud. Any individual point can sit far from it, and on an R-squared of 0.0097 almost every point does.
A relationship through time. A cross-section on one date says how companies differ from each other today. It does not say what happens to one company as its gross margin changes.
The rule
Never quote a slope without its R-squared. A slope alone is an assertion that a relationship exists. R-squared is the number that says whether the relationship is worth acting on, and the two together take no more room than one.
Check yourself
A regression gives a slope of 0.1476 and an R-squared of 0.0097. What has been established?
- That gross margin drives net margin, weakly
- That a line can be fitted, and it accounts for under 1 percent of the variation
- That there is no relationship at all
Show the answer
Answer: B.
A slope always exists. R-squared says how much of the outcome's variation the line accounts for, and 0.0097 means almost none of it, whatever the slope looks like.What does R-squared measure?
- How likely the slope is to be real
- The share of the outcome's variation the fitted line accounts for
- The size of the effect
Show the answer
Answer: B.
It is a share of variation, from 0 to 1. Whether the slope is distinguishable from zero is the p-value's question, and how large the effect is, is the slope's.A regression on a cross-section of companies gives a strong fit. What does that tell you about one company over time?
- That the same relationship holds within that company
- Nothing: a cross-section describes how companies differ from each other on one date
- That the relationship is causal
Show the answer
Answer: B.
Differences across companies and changes within one company are separate questions. A fit on one says nothing about the other, and treating them as interchangeable is a standard error in applied work.Sources
- Regressions computed across active US equity listings, read from this product's own store on 16 September 2026. Net margin on gross margin: 2,604 listings, slope 0.1476, intercept minus 12.056, R-squared 0.0097. Return on equity on return on invested capital: 2,001 listings, slope 0.9763, intercept 0.691, R-squared 0.5411.
What this leaves out
- Both regressions are computed on bounded ranges of each variable, stated in the sources, so that extreme values do not set the line on their own. A different bound gives different coefficients.
- Both are cross-sections on one date. Neither supports a claim about any company through time.
- A straight line is imposed here because the lesson is about what a line can support. A relationship that is not straight would be misdescribed by all three outputs, and the R-squared would not necessarily reveal it.
- These count listings, not deduplicated companies.
- Nothing here is advice about any security.