Correlation & regression
Lines of best fit, residuals, and what r means.
Pen and paper is fine · no calculator needed why?
Opens at level 43.
Lesson and untimed practice
Read the full lesson and try each skill without a clock. About 3 minutes to read.
skills · practice stats
-
Predict from a line not tried yet
worked example
A fitted line says score = 29 + 3.6 × hours. What does it predict for score when hours = 10?
Answer: 65
- 29 + 3.6 × 10 = 29 + 36 = 65.
-
Residual not tried yet
worked example
A line predicts ŷ = 17 + 5x. At x = 3 the actual y is 29. What is the residual (actual minus predicted)?
Answer: -3
- Predicted: 17 + 5 × 3 = 32.
- Residual = actual − predicted = 29 − 32 = −3.
-
Read a correlation not tried yet
worked example
Across weeks, the correlation between ad spending and website visits is 0.6. Which statement fits best?
- moderate negative linear relationship
- very weak positive linear relationship
- no relationship
- more ad spending causes 60% more visits
- moderate positive linear relationship
Answer: moderate positive linear relationship
- r = 0.6: the sign is positive (weeks with more ad spending tend to have more visits), and its size is in the middle: a clear but loose straight-line pattern.
- That’s a moderate positive linear relationship. Correlation alone doesn’t prove cause, and r is not a percent.
-
Slope from r not tried yet
worked example
The correlation between x and y is −0.6. The standard deviation of y is 18 and the standard deviation of x is 14. What is the slope of the least-squares line for predicting y from x? Round to 2 decimal places.
Answer: -0.77
- b = r × s_y ÷ s_x = −0.6 × 18 ÷ 14
- = −10.8 ÷ 14 ≈ −0.7714, which rounds to −0.77.
rest ladder
- 1 day
- 3 days
- 7 days
- 14 days
- 30 days
- 60 days
- mastered · every 90 days