Terrence created a scatter plot to represent the total number of goals scored by each player on his soccer team in a season and the number of hours the player spent at soccer practice.

Question

The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35.

Which graph shows the line of best fit for the data in Terrence's scatter plot?

A. The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (26, 30) and (45, 22).

B. The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (10, 0), (59, 26) and (70, 32).

C. The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (55, 26) and (59, 26).

D. The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (25, 16) and (55, 26).

GPT-4o mini · Answer

To determine which graph shows the line of best fit, we need to find a trend that best represents the relationship between the hours spent at soccer practice (x-values) and the goals scored (y-values). A line of best fit should generally pass through the center of the data points and represent the overall trend.

Let's analyze the options provided:

Option A: The line passes through points (26, 30) and (45, 22). This suggests that as practice hours increase from 26 to 45, the goals scored decrease from 30 to 22, indicating a negative correlation, which does not typically reflect a positive relationship between practice and goals.
Option B: The line passes through points (10, 0), (59, 26), and (70, 32). This suggests that as practice hours increase, goals scored also increase, reflecting a positive correlation. This would typically be expected in a situation where more practice leads to more goals scored.
Option C: The line passes through points (55, 26) and (59, 26). This indicates that between the hours of 55 to 59, the number of goals scored remains constant at 26, which suggests no change and does not reflect the overall trend of most data points.
Option D: The line passes through points (25, 16) and (55, 26). This indicates a positive trend where more practice hours correlate with more goals scored.

Based on this analysis, Option B reflects a consistent positive trend where the number of goals scored increases with hours of practice, which is most suitable as a line of best fit for Terrence's scatter plot.

Therefore, the answer is Option B.