Question

1. give a value for r that would indicate that a line of best fit has a positive slope and the variables are strongly correlated.
2. the size of a district and the number of parks in it have a weak positive relationship.

explain what it means to have a weak positive relationship in this context.

Explanation:

Step1: Define strong positive r range

The correlation coefficient $r$ ranges from $-1$ to $1$. A strong positive correlation corresponds to $r$ values close to $1$, typically $0.7 < r \leq 1$.

Step2: Select valid r value

Choose a value within this range, e.g., $r = 0.85$.

For the weak positive relationship: A weak positive relationship means that as the size of a district increases, the number of parks in it tends to increase, but this trend is not consistent or strong. There is a loose, not tight, upward pattern when plotting district size against number of parks, and many data points will deviate from a clear upward line.

Answer:

1. $r = 0.85$ (any value between 0.7 and 1 is acceptable)
2. As district size increases, the number of parks tends to increase, but the trend is not strong, with many data points deviating from a clear upward pattern.