The scatterplot shows a company’s monthly spending on digital advertisements and the number of new customers gained that month. The solid line is a line of best fit. The point labeled represents one month.
In the month represented by , each new customer generated $30 in first-month revenue. According to the line of best fit, the actual first-month revenue for that month was how much greater than the revenue predicted by the model?
Which choice is the best answer?
For a scatterplot question involving a line of best fit, first use convenient points on the drawn line to determine the model’s predicted value at the relevant horizontal coordinate. Then compare that prediction with the actual plotted point. Carefully interpret axis scales before converting the resulting difference into the requested contextual quantity.
Hints
Use the line, not just the point
Use the two labeled points on the solid line to determine the line’s change in new customers for a change in ad spending.
Compare at the same spending value
Find the line’s predicted vertical-coordinate value when the horizontal coordinate is , then compare it with point .
Interpret the vertical scale
The vertical axis is measured in hundreds of customers. Convert the difference to individual customers before using the $30 per-customer value.
Desmos Guide
Use algebra first
Finding the rise over run from the two labeled points is faster than using Desmos for this question. Desmos can verify the predicted value and revenue difference.
Define the line
Enter , the equation determined from the labeled points on the line of best fit.
Check the prediction and difference
Enter to find the line’s predicted vertical-coordinate value at . Then enter on an expression line to verify the revenue difference.
Step-by-step Explanation
Find the model’s rate of change
The labeled points on the line of best fit are and . Thus, the line rises by vertical-axis units over horizontal-axis units, so its slope is hundreds of customers per thousand dollars of ad spending.
Predict the number of customers
At , the line predicts
The model therefore predicts hundreds, or new customers.
Compare the actual and predicted values
Point has vertical coordinate , so the actual number of new customers was . The actual number exceeded the prediction by
customers.
Convert the customer difference to revenue
Each of the additional customers generated $30 in first-month revenue. Therefore, the actual revenue was , or $15,000, greater than the model’s prediction.