Question

the scatter plot shows the time an athlete spends practicing and the number of hours of free time each week.

use technology to write a line of best fit equation and predict the amount of free time, to the nearest hour, for an athlete who practices 9.5 hours per week.

1 hour
3 hours
2 hours
4 hours

Explanation:

Identify data points from the scatter plot

The coordinates \((x, y)\) representing (Practice, Free Time) are:

$$ (1, 7), (1, 8), (2, 9), (3, 6), (4, 9), (5, 5), (5, 6), (6, 7), (7, 4), (8, 7), (9, 4), (10, 2) $$

Calculate the line of best fit

Using linear regression formulas:

$$
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$$

The line of best fit equation is:

$$ y \approx -0.517x + 8.795 $$

Predict free time for 9.5 hours of practice

Substitute \(x = 9.5\) into the regression equation:

$$ y \approx -0.517(9.5) + 8.795 \approx -4.9115 + 8.795 = 3.8835 $$

Rounding to the nearest hour gives:

$$ y \approx 4\text{ hours} $$

Answer:

• 1 hour
• 3 hours
• 2 hours
• 4 hours (Correct answer)