A table of measurements that roughly follows a straight trend calls for a linear regression, a line fitted to all the data. Put the quantity you know in the input column and the quantity you want to predict in the output column. Fit a line in Desmos, then evaluate it at the requested input. Use the line’s prediction, not a nearby recorded value.
Hints
- Hint 1
Temperature is the input because you’re given a temperature and asked to predict chirps. The chirping rate is the output, the number the model predicts. Which Desmos table column should hold each?
- Hint 2
A linear regression fits a line to all the measured pairs, even if the line misses some individual points. After Desmos finds the line’s slope and intercept, how can you use them to predict chirps at 68°F?
Step-by-step
Fit a line in Desmos
Step 1Pair each temperature with its chirping rate
The question predicts chirps from temperature, so put temperatures in Desmos’s column and chirps per minute in its column. Enter each pair in the same row; swapping the columns would predict temperature from chirps instead.
- Step 2
Fit the linear model
Type . The tilde tells Desmos to fit a line to the table; is its slope and is its intercept. Under PARAMETERS, Desmos shows and . The recorded chirp counts don’t lie exactly on one line, so use this best-fit line rather than treating any one row as the rule.
- Step 3
Predict at 68°F
Type so Desmos uses the fitted values it stored. It shows , which is closest to 92. So the best estimate at is 92 chirps per minute. Choice B.