Predicting an exam score from homework completed

Question

A teacher models the final exam score against the number of homework sets a student completed:

$\widehat{\text{score}} = 45 + 5 \cdot (\text{homework sets completed}).$

What score does the model predict for a student who completed 8 homework sets?

Accepted Answer

Put the input, 8 homework sets, into the fitted line: \widehat{	ext{score}} = 45 + 5 	imes 8 = 45 + 40 = 85 	ext{ points.} The intercept 45 is where the line starts (the model's guess for a student who did no homework), and the slope 5 adds five points per completed set. Eight sets gives a predicted score of 85. This is a best-guess average, not a certainty: two students who both finished eight sets could still score differently. The line predicts the center of what such students tend to score. Takeaway. Substitute and evaluate: 45 + 5 	imes 8 = 85, a predicted average rather than a guara…

Predicting an exam score from homework completed

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