Question

in 8 - 10, draw a line from each scatter plot to the best description of its association and then to the variables it would most likely represent. not all choices will be used.
8.
9.
10.
positive and linear
positive and non - linear
negative and linear
negative and non - linear
no association
the temperature outside and the total gallons of gas sold at a gas station
the altitude of a hiker and the total oxygen level in the air
the size of a home and the cost of monthly utilities for the home

Explanation:

Step1: Analyze scatter - plot 8

The points in scatter - plot 8 are randomly distributed. So, it has no association.

Step2: Analyze scatter - plot 9

As the \(x\) - values (independent variable) increase, the \(y\) - values (dependent variable) also increase in a non - linear way. So, it has a positive and non - linear association. The size of a home and the cost of monthly utilities for the home: as the home size increases, the utility cost increases (positive), but not in a linear fashion (more rooms might not mean a strictly linear increase in cost due to factors like energy - efficient appliances etc.), so it matches scatter - plot 9.

Step3: Analyze scatter - plot 10

As the \(x\) - values increase, the \(y\) - values decrease. The altitude of a hiker and the total oxygen level in the air: as altitude (\(x\)) increases, oxygen level (\(y\)) decreases. And the relationship is non - linear (oxygen levels don't decrease at a constant rate with altitude), so scatter - plot 10 has a negative and non - linear association.

Answer:

1. No association
2. Positive and non - linear; The size of a home and the cost of monthly utilities for the home
3. Negative and non - linear; The altitude of a hiker and the total oxygen level in the air