Question

6
5
4
3
2
1
0
0 1 2 3 4 5 6
x
there is a positive correlation in the data set.
there is a negative correlation in the data set.
there is no correlation in the data set.
more points are needed to determine the correlation.

Explanation:

Step1: Analyze positive correlation

In a positive correlation, as \(x\) - values increase, \(y\) - values also tend to increase. Looking at the scatter - plot, we can see that there is no clear upward trend where an increase in \(x\) consistently leads to an increase in \(y\).

Step2: Analyze negative correlation

In a negative correlation, as \(x\) - values increase, \(y\) - values tend to decrease. In the given scatter - plot, there is no clear downward trend where an increase in \(x\) consistently leads to a decrease in \(y\).

Step3: Check for no correlation

A lack of correlation means that there is no discernible pattern (neither positive nor negative) between the \(x\) and \(y\) values. In the given scatter - plot, the points are scattered in a way that does not follow a linear (positive or negative) pattern.

Answer:

There is no correlation in the data set.