Question 50·Medium·Two-Variable Data: Models and Scatterplots
A weather technician records the altitude of a weather balloon, (in thousands of feet), and the outside air temperature, (in degrees Fahrenheit). Each dot in the scatterplot represents one measurement.
Which equation could represent a reasonable line of best fit for the data shown?
For a best-fit line from a scatterplot, first determine whether the trend is increasing or decreasing (sign of the slope). Then estimate the slope using two widely separated points on the trend and estimate the intercept by looking near . Match the choice that best agrees with both estimates.
Hints
Decide whether the slope should be positive or negative
As (altitude) increases, the points go downward, so the line of best fit should have a negative slope.
Estimate slope using endpoints
Pick one point near the left end of the trend and one near the right end, then compute .
Use to estimate the intercept
Look at the points near to estimate the temperature when altitude is 0.
Desmos Guide
Enter the points
In Desmos, create a table and enter the values from the scatterplot.
Graph the answer-choice lines
Enter each equation from the choices (one per line) so you can see them on the same axes as the data.
Decide which line balances the points
Pick the line that runs through the middle of the cluster with roughly as many points above as below across the full -range.
Step-by-step Explanation
Estimate the slope from two far-apart points on the trend
Use two points that are far apart and lie close to the overall trend, such as and .
So the line of best fit should have a slope close to (temperature decreases as altitude increases).
Estimate the -intercept
At , the data are near , so the -intercept should be about .
Choose the equation that matches both estimates
The equation with slope and -intercept is .