The scatterplot shows the daily energy produced by a solar panel system for different amounts of sunlight. The solid line is a line of best fit. Each choice gives the coordinates of a plotted data point.
Which choice identifies the data point for which the observed energy production is the greatest percent greater than the energy production predicted by the line of best fit?
For a scatterplot question involving percent above or below a line of best fit, first use clearly marked points on the line to write a model. Then calculate a relative residual, not just a residual: divide the vertical difference by the predicted value. This prevents choosing a point that is far above the line but has a smaller percentage increase because its predicted value is also large.
Hints
Use the marked points on the line
Use the two labeled points on the line of best fit to find its slope and equation.
Focus on percent greater
A larger vertical distance above the line does not always mean a larger percent greater value. Divide each positive residual by the value predicted by the line.
Compare ratios
For each answer choice, substitute its sunlight value into the line's equation before calculating the relative difference.
Desmos Guide
Enter the line model
Algebra is quick here. For a Desmos check, enter , using the two labeled points on the line of best fit.
Enter the candidate points
In a table, enter the four candidate sunlight values in one column and their observed energy values in a second column.
Compare relative residuals
Create a third column with . Desmos displays the four relative differences; select the point corresponding to the largest positive value.
Step-by-step Explanation
Find the line's equation
The line passes through and . Its slope is , so its equation is .
Calculate relative differences
For each choice, find . The ratios are for , for , for , and for .
Compare the percentages
The ratio is the greatest of the four. Therefore, the point with the greatest percent greater observed energy production is .