A table of measured pairs and a named linear model call for a least-squares regression: a line fitted to the overall trend. Enter the paired data in Desmos, fit the line, then use it to predict at the requested input. The line uses all the data, so a line through two selected points can give a different prediction.
Hints
- Hint 1
The input is what you start with to make a prediction. Because the teacher predicts scores from hours studied, which values belong in Desmos’s input column, and which belong in its output column?
- Hint 2
A linear regression fits a line to paired data. In Desmos, the tilde in tells it to find the line that best fits all eight pairs, rather than a line through two chosen students.
- Hint 3
A prediction comes from the fitted line, not directly from a recorded score. Once Desmos finds and , what do you get by putting the requested number of hours into ?
Step-by-step
Fit the line in Desmos
Step 1Pair each hour with its score
The teacher predicts scores from hours studied, so hours are the input and scores are the output. Enter hours in Desmos’s column and scores in its column. Keep each student's hour and score in the same row; for example, hour pairs with , not .
- Step 2
Fit the line the teacher specified
Type . The tilde tells Desmos to run a least-squares regression: it chooses the line that makes the total of the squared misses from the recorded scores as small as possible. Under PARAMETERS, Desmos reports and . Fit all eight pairs, not just two points that look convenient.
- Step 3
Predict the score at 8 hours
The question asks for the model’s score at hours, so type on a new line. Desmos uses its stored fitted values and returns about . That is a predicted score, not a score taken from a table row. The best prediction is . Choice C.