A five-minute idea, no math required

R-squared:
how good are our guesses?

One little number, between 0% and 100%, that tells us how much to trust a prediction.

Meet Rosa's ice cream stand

Rosa notices something: on hotter days, she sells more ice cream.

Each dot is one day — how hot it was, and how much she sold.

Question: can she use the weather forecast to predict tomorrow's sales?

Hotter day → more sales (usually)

We draw a line through the dots

The line is our prediction rule: pick tomorrow's temperature, read off the expected sales.

But look — the dots don't sit exactly on the line. Real life is messy.

So the natural next question is: how close are the dots to the line, overall?

The line = our prediction rule

That's exactly what R-squared measures

R-squared is a score from 0% to 100% for how well the line matches the dots.

Think of sales going up and down from day to day. R-squared answers: how much of that up-and-down does our line account for?

0% — the line tells us nothing100% — the line nails it

If R-squared is 85%, temperature accounts for 85% of the day-to-day change in sales. The other 15% is everything else — a school trip, a rainy hour, plain luck.

See it move

R² = —

Drag the slider and watch the score.

How messy is real life?

Tidy dotsScattered dots

Same line — the dots decide the score

So what does the number mean?

≈ 90%

Excellent fit. Predictions from this line will usually be close. Plan tomorrow's stock with confidence.

≈ 50%

Half the story. The line helps, but plenty of other things matter too. Use it as a rough guide.

≈ 10%

Barely better than guessing. Temperature alone can't predict sales here — look for other explanations.

What counts as "good" depends on the field: 50% might be superb for predicting people, and weak for a factory machine.

Why do we use R-squared?

🤝

To know how much to trust a prediction

Before betting money or time on a forecast, it tells us how solid the ground is.

⚖️

To compare explanations fairly

Does temperature predict sales better than the day of the week? Compare the two scores.

💬

To share one honest number

"Our model explains 85% of the variation" — anyone can understand that, no charts required.

Two honest warnings, then we're done

A high score doesn't prove cause. Ice cream sales and sunburns rise together — ice cream doesn't cause sunburn. The sun causes both.

A low score isn't failure. It's useful news: it says "this one ingredient isn't the whole recipe."

The takeaway: R-squared is a 0–100% score for how well our prediction line fits reality — so we know how much to trust it, and when to keep looking.

Thank you! Questions welcome.