Math 1 · Unit 10
Linear and Exponential Regression
Five lessons: scatter plots and correlation, the line of best fit, residuals, exponential regression, and association against causation. Real data is messy, so you find the line or exponential curve that fits best, read its numbers in the story, and remember that every model is a little bit wrong.
Scatter Plots and Correlation
Real data only comes close to a line or curve. Describe a scatter plot by direction, form, and strength, then meet the correlation coefficient r, a number from negative 1 to 1: the sign is the direction, the size is the strength. Build a scatter plot and watch r change, and match r values to plots.
Start Unit 10, Lesson 1The Line of Best Fit
The least squares regression line is the member of the line family that comes closest to the points. Eyeball a line, then check it against the tool. Read the slope and y-intercept in the story with the lab rat, predict forward and backward, and learn why predictions far outside the data can be nonsense.
Start Unit 10, Lesson 2Residuals, Checking the Fit
A residual is actual minus predicted, the vertical gap between a point and the line. Plot all the residuals: random scatter around 0 means a line fits, a pattern means the data is curved. The gnats show the surprise, a line with r of about 0.98 whose residuals still make a U. Use the scatter plot, r, and the residual plot together.
Start Unit 10, Lesson 3Exponential Regression
When the ratios are roughly constant and the plot bends, fit an exponential. The gnats: about 12.48 times 1.63 to the x, growing about 63% an hour, reaching 200 at about 5.7 hours. The pennies: about 348 times 0.49 to the x, close to the story's one half. Switch between the linear and exponential fits and see which follows the points.
Start Unit 10, Lesson 4Association Is Not Causation
Two things can move together without one causing the other. It may be coincidence, like Spelling Bee words and spider bites, or a lurking variable, like the money behind Larry's cars or the sunny weather behind ice cream and sunburns. Showing cause takes a designed experiment with random groups, not just a strong r.
Start Unit 10, Lesson 5Printables for Unit 10
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.