Question

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

For the equation \(y = 0.39x+20.23\) (Home - Runs set), the slope \(m = 0.39>0\), so it has a positive correlation. For the equation \(y=0.15x - 23.2\) (Runs set), the slope \(m = 0.15>0\), so it also has a positive correlation.

Step2: Compare the rates of change

The rate of change of a linear equation \(y=mx + b\) is given by the slope \(m\). For the Home - Runs set, \(m_{HR}=0.39\). For the Runs set, \(m_R = 0.15\). Since \(0.39>0.15\), the Home - Runs set has a greater rate of change.

Answer:

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