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Session 13: Charting & Trendlines

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Session 13

Charting & Trendlines

(Last session of the Foundations unit)

Why Plot?

A table of numbers can hide a lot — an outlier, a pattern, data that doesn't behave quite the way you expected.

A plot makes it visible at a glance.

Building the Plot

  1. Scatter plot: weight vs. displacement
  2. Add a linear trendline
  3. Display the equation
  4. Display R²

The Slope Tells You the Relationship

The slope of this line tells you the rate one thing changes relative to the other.

For a launcher, that's the whole idea behind calibration.

R² — What It Tells You

Closer to 1 = tighter fit.

R² — What It Tells You

It's diagnostic information, not a pass/fail grade — same idea as last session's conditional-formatting flags.

If R² Is Low — Don't Just Move On

Ask:

  • Were a couple trials noisy? (measurement problem)
  • Does the data genuinely behave non-linearly here? (real effect)

Different problems, different fixes.

Now Actually Use It

A trendline you only look at is a picture. A trendline you predict with is a tool.

Now Actually Use It

Your equation looks something like:

y = 0.8x + 2

Forward: pick a weight you never tested, plug it in for x, and you get a predicted displacement.

The Harder Direction

Calibration usually runs backwards. You don't ask "what happens at this setting" — you ask "what setting do I need to hit this?"

The Harder Direction

Want a displacement of 10? Solve for x:

10 = 0.8x + 2

8 = 0.8x → x = 10

That's the entire skill Field Test Day runs on. Practice it today, on a spring, where nothing's at stake.

Then Check Yourself

Predicting isn't the last step. Go measure it and see how close you actually got.

That gap — predicted vs. actual — is the only honest measure of whether your model is any good.

You Could Also Compute This Directly

=SLOPE(y-range, x-range)

You Could Also Compute This Directly

=RSQ(y-range, x-range)

The chart isn't magic — it's the same functions skill from Session 12, just drawn as a picture.

Submit Today

Data table + plot + trendline + R² + a one-sentence diagnostic note on your fit quality.

Watch Out For

  • Treating R² as a grade instead of information
  • Assuming low R² always means "redo the experiment"
  • Confusing the trendline's slope with individual data points

That's the Last New Skill in This Unit

Define, Design, Notebook, Safety, Measurement, Functions, Data Quality, Conversion, Tolerance, and now Charting — all of it was building toward one thing.

Next Up

The Launcher Project begins.

Same measure → log → chart workflow. Real stakes. Your own launcher.

'F' → Fullscreen

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Build

Step 1: Build the Plot

Using your Session 11–13 data, create a scatter plot of weight vs. displacement in Sheets.

Step 2: Add the Trendline

Fit a linear trendline. Display its equation and its R² value.

Step 3: Diagnose Your Fit

If your R² is low, don't just move on — decide whether it looks like a measurement problem (a couple of noisy trials) or a real effect (the data genuinely isn't linear across this range). If Session 12 flagged a row, check whether it's the source of any weakness in your fit.

Step 4: Predict Forward

Pick a weight you never tested, somewhere inside the range you did test. Use your trendline equation — not your eyes on the chart — to predict its displacement. Write the prediction down.

Step 5: Predict Backward

Now the direction calibration actually uses. Pick a displacement you never measured, inside your tested range. Solve your equation for x to find the weight that should produce it. Write down both the target and the weight you calculated.

Step 6: Test Both Predictions

Actually hang both weights and measure what you get. Record predicted vs. actual for each, and the difference.

PredictionPredictedActualOff by
Step 4 (forward)
Step 5 (backward)

Step 7: Write Your Diagnostic Note

One sentence: is your fit strong or weak, and if weak, do you think that's from measurement noise or a real effect? Reference how close your two predictions actually landed.

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Checkpoint

Your submitted Sheets file must include all of the following:

  • Raw data table (from Sessions 11–13) — trials, weights, displacements, units
  • Scatter plot of weight vs. displacement
  • Trendline with displayed equation and R² value
  • Both predictions — forward and backward — with predicted vs. actual recorded, and how far off each was
  • One-sentence diagnostic note: is your fit strong or weak, and if weak, do you think that's from measurement noise or a real effect?

The backward prediction is the one that matters most — it's the exact operation Field Test Day will ask you to do under pressure, with a target you've never seen.

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Reflection

Answer these on your own. Reflections are individual, even when the rest of the session was team work.

  1. What would it take to convince you your fit was actually wrong, even if R² looked good?
  2. This is the last new skill in Foundations. Looking back at Define, Design, Notebook, Safety, Measurement, Functions, Data Quality, Conversion, Tolerance, and now Charting — which one do you think you'll rely on most once the Launcher Project starts?
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Submit

Submit your data table, plot, trendline, R², and diagnostic note.

Activity Complete