Question

the scatter plot with the line of best fit below shows data taken from 15 athletes. what is the closest estimate for the r-value, and how does it relate to the data and line of best fit? the r-value is close to 1 because there is a weak correlation between the line of best fit and the data. the r-value is close to 0 because there is a strong correlation between the line of best fit and the data. the r-value is close to 0 because there is a weak correlation between the line of best fit and the data. the r-value is close to 1 because there is a strong correlation between the line of best fit and the data.

Explanation:

Step1: Recall r - value meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. \( r \) ranges from - 1 to 1. If \( r\approx1 \), there is a strong positive linear correlation; if \( r\approx - 1 \), strong negative; if \( r\approx0 \), weak or no linear correlation.

Step2: Analyze the scatter plot

In the given scatter plot, the data points are close to the line of best fit, and the line has a positive slope. So the linear relationship is strong and positive.

Step3: Evaluate the options

• Option 1: Says \( r\approx1 \) with weak correlation. Wrong, since close to line means strong.
• Option 2: Says \( r\approx0 \) with strong correlation. Wrong, \( r\approx0 \) is weak.
• Option 3: Says \( r\approx0 \) with weak correlation. But data is close to line, so strong. Wrong.
• Option 4: Says \( r\approx1 \) with strong correlation. Matches the analysis (data close to line, positive slope, strong positive correlation).

Answer:

The r - value is close to 1 because there is a strong correlation between the line of best fit and the data.