Question

compare these data sets. the equation of the trend line is listed below each data set.

hr	av
198	84
149	88
148	81
138	88
137	75
131	81
118	88
103	95

$y = 0.36x + 20.23$

r	av
798	84
655	86
634	81
627	88
619	75
613	81
608	89
583	56

$y = 0.15x - 23.2$

which statements are true about these data sets? check all that apply.

• ☐ both sets have negative correlation.
• ☐ both sets have positive correlation.
• ☐ there is no correlation between the sets.
• ☐ the runs set has a greater rate of change than the home runs set.
• ☐ the home runs set has a greater rate of change than the runs set.

Explanation:

Step1: Analyze Correlation Type

For a positive correlation, as \( x \) increases, \( y \) increases. In both data sets, when \( x \) (HR or R) values change, \( y \) (W) values show an upward trend (checking the trend lines: \( y = 0.36x + 20.23 \) and \( y = 0.15x - 23.2 \) have positive slopes). So both have positive correlation. Negative correlation would have negative slopes, and no correlation would have near - zero slopes, so first and third options are wrong, second is correct.

Step2: Analyze Rate of Change (Slope)

The rate of change is the slope of the trend line. For Home Runs (first set) trend line: slope \( m_1 = 0.36 \). For Runs (second set) trend line: slope \( m_2 = 0.15 \). Since \( 0.36>0.15 \), the Home Runs set (first) has a greater rate of change than the Runs set (second). So the fifth option is correct, fourth is wrong.

Answer:

B. Both sets have positive correlation.
E. The Home Runs set has a greater rate of change than the Runs set.

(Note: Assuming options are labeled as A - E with A: Both sets have negative correlation, B: Both sets have positive correlation, C: There is no correlation between the sets, D: The Runs set has a greater rate of change than the Home Runs set, E: The Home Runs set has a greater rate of change than the Runs set)