Tables & Regression
Data-interpretation questions become one-step problems. Enter the data, let Desmos fit the model, and read the answer off the output.
Creating a table
- Click the + button at the top of the expression list and pick table.
- Two columns appear labeled $x_1$ and $y_1$. Type your data, tab between cells, enter for new rows.
- Points plot live on the graph as you type.
Use the table whenever a question gives you paired data (like a regression problem, or "use the table to find...").
Linear regression (line of best fit)
Problem: A scientist records the growth of a plant every week.
Week: 1, 2, 3, 4, 5 Height (cm): 4.2, 6.5, 8.9, 11.0, 13.4
Which linear function best models the height after $t$ weeks?
- Create a table. Label $x_1$ = weeks, $y_1$ = heights. Enter the 5 rows.
- On a new expression line, type the regression syntax:
y_1 ~ m*x_1 + b (the tilde means "fit").
- Desmos shows the fitted values below: $m \approx 2.29$, $b \approx 1.99$, $r^2 \approx 0.999$.
- The model is $y = 2.29x + 1.99$, pick the answer choice closest to that.
The $r^2$ value tells you fit quality (1 = perfect). Values above $0.95$ are a great fit.
Exponential regression
Problem: A bacterial population doubles approximately every hour. After 1, 2, 3 hours there are 50, 100, 205 cells. Which function best models the growth?
- Create a table with the $(1, 50), (2, 100), (3, 205)$ pairs.
- Type
y_1 ~ a*b^{x_1}.
- Desmos reports $a \approx 25.1$, $b \approx 2.02$. Model: $P(t) = 25.1 \cdot 2.02^{t}$.
Match to the nearest answer choice. $b$ close to $2$ confirms "doubles every hour."
Quadratic regression
For a parabolic fit:
- Regression syntax:
y_1 ~ a*x_1^2 + b*x_1 + c.
- Common on projectile-motion or profit-curve word problems.
Worked example: prediction from a model
Problem: Using the linear plant-growth data above, predict the height at week 7.
- After running the regression, type a new expression:
y = 2.29x + 1.99 (with the actual fitted values).
- Type
x = 7 on a new line, Desmos draws a vertical line. Click the intersection with the fitted line.
- Label reads $(7, 18.0)$. Height at week 7 $\approx 18$ cm.
Common traps
Watch for these gotchas
- Subscript typos.
y1 and y_1 are different. Table columns are x_1, y_1. Use the underscore.
- $\sim$ vs. $=$. Regression uses tilde (
~). Equals gives you an equation, not a fit.
- Wrong model family. A linear fit to exponential data gives low $r^2$. If the fit looks bad, try $a \cdot b^x$ or $a \cdot x^2 + b \cdot x + c$.
- Rounding matters. Some answer choices differ only in the decimal. Use at least 2–3 sig figs when matching.
Try it yourself
Practice problem
A cafe tracks daily coffee sales for 5 weekdays:
Day: 1, 2, 3, 4, 5 Cups sold: 42, 49, 58, 63, 70.
Fit a linear model. What is the predicted number of cups sold on Day 8? (Round to the nearest whole number.)
Show answer
Steps: Add a table, enter $x_1$ = 1..5 and $y_1$ = 42, 49, 58, 63, 70. New line: y_1 ~ m*x_1 + b. Desmos reports $m \approx 7.1$, $b \approx 34.7$. Predicted at $x = 8$: $7.1 \times 8 + 34.7 \approx 91.5$. Answer: $92$ cups.
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