Question

7 multiple choice 1.25 points a sample of 10 students was taken from a history class. their final exam scores, y, and the number of hours they studied, x, before the exam was noted. the least-squares regression line is given to be \\(\widehat{y} = 4.82x + 56.56\\) interpret the slope. \\(\bigcirc\\) for each additional hour of studying, the final exam score increases by 4.82 points on average. \\(\bigcirc\\) for each point increase on the final exam, the number of hours studied increases by 4.82 hours. \\(\bigcirc\\) for each additional hour of studying, the final exam score increases by 56.56 points on average. \\(\bigcirc\\) if a student does not study at all then the final exam score will be 56.56 points.

Explanation:

The regression line is in the form $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the intercept. The slope $m=4.82$ represents the average change in $\hat{y}$ (final score) per unit change in $x$ (study hours). Thus, each additional hour of studying is associated with an average 4.82-point increase in the final score.

Answer:

For each additional hour of studying, the final exam score increases by 4.82 points on average.