Thinkabara

📈 Intro to Statistics · Lesson 5 of 7

Correlation and regression

Google Classroom

Scatterplots, r, the line of best fit — and causation.

Scatterplots first

Always plot two quantitative variables before calculating anything. Look for direction (positive/negative), form (linear/curved), strength, and outliers.

The correlation coefficient r

Range−1 to +1
r near +1Strong positive linear relationship
r near −1Strong negative linear relationship
r near 0No linear relationship (there may still be a curved one)
No unitsChanging units doesn’t change r

The regression line

The least-squares line ŷ = a + bx predicts y from x. Example: predicting exam score from hours studied, ŷ = 58 + 4.5x. The slope means: each extra hour of study is associated with 4.5 more points, on average. Someone who studies 6 hours is predicted to score 58 + 27 = 85.

r² and limits

r² is the fraction of the variation in y explained by the line (r = 0.8 → r² = 0.64, so 64%). Don’t extrapolate far beyond your data (20 hours of study doesn’t predict 148 points), and remember: correlation is not causation — a lurking variable may drive both.

In a spreadsheet

=CORREL(A2:A21, B2:B21)   → r
=SLOPE(B2:B21, A2:A21)    → b
=INTERCEPT(B2:B21, A2:A21) → a

Or insert a scatter chart and add a trendline.

✏️ Practice: your turn

  1. Make a scatterplot of hours slept vs. a mood score for 10 days
  2. Estimate r by eye, then compute it with =CORREL
  3. Interpret the slope of a regression line in a sentence
  4. Name a possible lurking variable for “ice cream sales and drownings”

✏️ Scientific calculator with a statistics tab (mean, median, standard deviation)

🧠 Quick quiz

Answer all 4 questions correctly to mark this lesson as done.

1. r = −0.9 means…
2. ŷ = 58 + 4.5x. Predicted score for 4 hours?
3. r = 0.7, so r² =
4. Strong correlation proves causation?

0 of 4 correct

All lessons in Intro to Statistics

  1. 🎲 1. Data, variables and samplingCategorical vs. quantitative, populations, samples and bias
  2. 🎯 2. Mean, median and modeMeasures of center, and which one to use when data are skewed
  3. ↔️ 3. Spread: range, IQR and standard deviationHow spread out the data are, and how to read a box plot
  4. 🔔 4. The normal curve and z-scoresThe 68–95–99.7 rule and comparing values on different scales
  5. 📉 5. Correlation and regressionScatterplots, r, the line of best fit — and causation
  6. 🎯 6. Confidence intervalsEstimate ± margin of error, and what “95% confident” means
  7. ⚗️ 7. Hypothesis tests and p-valuesNull and alternative, the p-value, significance and errors