Question

kai runs a small dog - walking business and is trying to understand how the number of dogs walked per day affects the total time spent walking. they kept track of how many dogs they walked and how long they were out each day.

question 1

what kind of association does the data show overall - positive, negative, or none? how do you know?

Explanation:

Step1: Analyze the trend

As the number of dogs (independent variable) increases, observe the general trend of the time spent walking (dependent variable).
Looking at the data: when the number of dogs goes from \(1\) to \(2\) (increase in \(x\)), time goes from \(25\) to \(36\) (increase in \(y\)); from \(2\) to \(3\), \(36\) to \(40\); from \(3\) to \(4\), \(40\) to \(52\); from \(4\) to \(5\), a slight dip (\(52\) to \(50\)), but then from \(5\) to \(6\), \(50\) to \(68\); \(6\) to \(7\), \(68\) to \(74\); \(7\) to \(8\), \(74\) to \(110\); \(8\) to \(9\), \(110\) to \(89\) (dip), \(9\) to \(10\), \(89\) to \(92\). Overall, as \(x\) (number of dogs) has an upward - moving tendency, \(y\) (time) also has an upward - moving tendency despite some minor fluctuations.

Answer:

The data shows a positive association. We know this because as the number of dogs (the independent variable) generally increases, the time spent walking (the dependent variable) also generally increases.