Question 38·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between weekly online advertising spending and the number of orders a small business received that week. A line of best fit is also shown.
Which choice best describes the meaning of the slope of the line of best fit in this context?
For slope-interpretation questions, first identify what 1 unit of represents (here, $100). Then find the slope of the line of best fit by using two clear points on the line and calculating rise over run. Finally, translate that numerical slope into words with the correct units (change in predicted for each increase of 1 unit in ).
Hints
Use the line, not the dots
Pick two clear points that the line of best fit goes through (not just nearby data points).
Compute rise over run
Find how much changes and how much changes between those two points, then compute .
Pay attention to the -axis units
The -axis is in $100s. Think about what an increase of 1 in means in actual dollars.
Desmos Guide
Enter the two points from the line
In Desmos, define two points on the line of best fit, for example:
Calculate the slope numerically
Compute the slope using an expression:
(Desmos will display a number for .)
Match the rate to the correct interpretation
Use the value of as “orders per 1 unit of ,” and remember that 1 unit of equals $100. Choose the statement that matches that rate and those units.
Step-by-step Explanation
Read two points on the line of best fit
From the graph, the line of best fit passes through approximately and .
Calculate the slope
So the predicted number of orders increases by about 5 for each 1-unit increase in .
Interpret the slope using the axis units
The -axis is measured in $100s, so an increase of 1 in means an additional $100 spent on ads. Therefore, the slope means that for each increase of $100 in ad spending, the predicted number of orders increases by about 5.
Answer: For each increase of $100 in ad spending, the predicted number of orders increases by about 5.