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Statistics 9-12 / Week 04 / Track Day
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Week 04 · Scatter Plots and Lines of Fit

Track Day

Track Day: a family line of fit
// Weeks of practice against laps run
⏱ about 20 min

Track Day: A Family Line of Fit

Saturday morning, a stack of index cards sits on the kitchen table beside a tape measure.

"Two cards, how tall?" Comet asks. "Then four, then six, up to twelve. Height in millimeters."

Wren measures each stack and reads the numbers. "What do you notice?"

"Almost a perfect line," someone says. "Each card adds the same little bit."

"That little bit is the slope," Comet says. "Millimeters per card. And the intercept should be near zero."

Nova hovers and glows a straight band through the dots. "Would you like a hint? Check the residuals before you trust the line."

"No pattern," Wren says. "The line fits. Our family just built a model."

  1. A scatter plot shows two quantitative variables, one dot per case. Read direction, form, strength and strays.
  2. The least-squares line makes the sum of the squared residuals smallest. Everyone gets the same line.
  3. The slope is the change in y for one more unit of x. The intercept is the value at x = 0, both in the data's units.
  4. A residual is observed minus predicted. A residual plot with no pattern means the line fits.
  5. Predict inside the data's range with care. Outside it, say the prediction is a stretch.
◇ FAMILY SCATTER PLOT
Pick two numbers that move together: cards in a stack and its height, or steps across a room and seconds.
Collect at least five pairs together and write them in a table.
Plot the dots on graph paper. Take turns saying direction, form, strength and strays.
Lay a pencil through the dots by eye. Find the slope in your units and say what it means.
Does the intercept make sense at x = 0? Decide together.
For a grown-up
Any walking or jogging for the timing is on a safe path, never a road, with you aware and water at hand.
The tape measure and the stopwatch are the only tools. Nothing heavy is lifted alone.
Ask your learner to explain the slope in your family's units. Saying it out loud is the goal.
ONE MORE LINE
  • Read the question.
  • Tap your answer.
The crew's practice line is laps = 0.94 × weeks + 1.89. What does it predict for 3 weeks of practice? (Round to 1 place.)
Your family stacked cards and measured height. Which variable goes on the x-axis?
The crew's practice line has a positive slope. For each extra week, do predicted laps go up or down? Type up or down.
WHY THIS EXERCISEThe sign of a slope is the quickest fact a line of fit gives you.
Draw your family scatter plot with its by-eye line. Write the slope in your units beside it.

A family model, built and explained. Next week: how tight is the cloud of dots, and what a pattern does not prove.

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