Question

question
ximena’s math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit.
calculate the residual for the data point that corresponds to 3 hours of study and a score of 72 points.
this is the only question in this section.

Explanation:

Step1: Recall Residual Formula

Residual is calculated as \( \text{Residual} = \text{Observed Value} - \text{Predicted Value} \). The observed value here is the quiz score of 72 (when study time \( x = 3 \) hours). The predicted value comes from the line of best fit at \( x = 3 \). From the graph, the line of best fit at \( x = 3 \) has a point \( (3, 78) \), so the predicted value \( \hat{y} = 78 \).

Step2: Calculate Residual

Substitute into the formula: \( \text{Residual} = 72 - 78 = -6 \).

Answer:

\( -6 \)