Residuals and Goodness of Fit
I can find residuals and read a residual plot to judge whether a line fits.
What students learn
Students learn to find each residual as actual minus predicted, plot the residuals, and read the plot: random scatter suggests a good linear fit, a pattern does not.
See inside
The key rule
Random scatter around 0 suggests a good linear fit. A clear pattern means a line is not the right model.
residual = actual − predicted
Judge the shape of the residual plot, not the sum of the residuals.
Watch out
For 8 points, a line of best fit gives residuals 7, 1, −3, −5, −5, −3, 1, 7. A student says a line is a good model because they add to 0.
The mistake: 7 + 1 − 3 − 5 − 5 − 3 + 1 + 7 = 0: good fitAdding to 0 says balanced, not straight.
The fix: signs: +, +, −, −, −, −, +, +: a UA pattern: the data curve, so not a line.
The mistakes it targets
- Judges the fit by the sum of the residuals
- Subtracts predicted minus actual
- Decides above or below by the size of y instead of the prediction
- Calls a residual plot a good fit when its dots form a pattern
- Drops a residual's sign when finding the actual value
- Thinks a residual plot with no pattern means exact predictions
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, six common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.