Cogito
Integrated Math 1 · Chapter 8 · Lesson 3
Scatterplots and Lines of Fit
Fitting a line to real data.
12 problems · about 22 minutes · S-ID.B.6, S-ID.C.7
What this lesson teaches
The student fits a line to bivariate data, interprets its slope, and uses residuals to judge fit.
- A line of fit runs through the middle of a scatterplot.
- Its slope predicts the change in y per unit of x.
- Residuals are actual minus predicted, and should scatter randomly.
Warm Up
Straightforward practice. Get the method working first.
5 problemsPredicted 30, actual 34. What is the residual?
Answer 4
Why 4.
What should a residual plot look like for a good linear model?
Answer Random scatter with no leftover pattern.
Why Random scatter.
y = 3x + 2 at x = 5. Predicted value?
Answer 17
Why 15 + 2.
Predicted 17, actual 14. Residual?
Answer -3
Why 14 − 17.
A negative residual means the model did what? 1 overestimated, 2 underestimated.
Answer 1
Why Predicted higher than actual.
Build It Up
The same ideas with more to keep track of.
3 problemsA model has slope 4 dollars per hour. Predicted rise for 3 more hours, in dollars?
Answer 12
Why 4 × 3.
y = 0.5x + 10 at x = 20. Predicted value?
Answer 20
Why 10 + 10.
Does a good line of fit prove causation? 1 yes, 0 no.
Answer 0
Why Association only.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the fitting process in order.
Answer 1. Plot the data as a scatterplot. 2. Check whether the pattern looks linear. 3. Fit a line through the middle of the cloud. 4. Check the residuals for a leftover pattern.
Why Residuals can only be checked once a line exists.
Predicted 25, actual 25. Residual?
Answer 0
Why They match exactly.
The Residual: Predicted 9, actual 11. What is the residual?
Answer 2
Why 2.
The Prediction: y = 2x + 1 at x = 6. What is the predicted value?
Answer 13
Why 13.