Question

which describes the scatterplot of a cars value compared to the age of the car?
there is no relationship between the age of a car and its value.
as the age of a car increases, its value increases.
as the age of a car increases, its value decreases.
as the age of the car decreases, its value decreases.

Explanation:

Step1: Analyze the trend of scatter - plot

In a scatter - plot, if one variable (age of car, \(x\)) and another variable (car's value, \(y\)) have a relationship. When we look at the general direction of the points. If the points tend to go from the upper left to the lower right, it indicates a negative correlation.

Step2: Relate the trend to the options

• Option 1: If there is no relationship, the points would be randomly scattered without any upward or downward trend. But here, there is a general downward trend (as \(x\) (age) increases, \(y\) (value) has a tendency to decrease), so this option is wrong.
• Option 2: If as the age (\(x\)) increases, value (\(y\)) increases, the points would tend to go from the lower left to the upper right. But our scatter - plot does not show this, so this option is wrong.
• Option 3: Since the points have a general trend where as \(x\) (age of car) increases, \(y\) (car's value) has a decreasing tendency (points go from upper left to lower right in a general sense), this option is correct.
• Option 4: If as the age (\(x\)) decreases, value (\(y\)) decreases, it would mean as \(x\) increases, \(y\) increases (opposite of what we want). But our scatter - plot shows as \(x\) increases \(y\) decreases, so this option is wrong.

Answer:

As the age of a car increases, its value decreases.