Question

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:

Analyze the distribution of data points

Using the Scatterplot Analysis knowledge point
We observe the coordinates of the plotted points on the scatterplot:

• Around \(x = 1\): points are at \(y \approx 2.4\) and \(y \approx 5.0\)
• Around \(x = 2\): points are at \(y \approx 2.3\), \(y \approx 3.0\), and \(y \approx 3.8\)
• Around \(x = 3\): points are at \(y \approx 2.1\), \(y \approx 3.0\), \(y \approx 3.4\), and \(y \approx 4.2\)
• Around \(x = 4\): points are at \(y \approx 1.5\), \(y \approx 3.0\), \(y \approx 4.4\), \(y \approx 5.1\), and \(y \approx 5.4\)

Determine the correlation trend

As \(x\) increases from \(1\) to \(4\), the \(y\)-values do not show a consistent upward or downward trend. Instead, they remain widely spread out across almost the entire vertical range (from \(y = 1.5\) to \(y = 5.4\)) at each interval of \(x\). There is no clear linear pattern or directional slope.

Evaluate the given options

• Positive correlation: Requires \(y\) to generally increase as \(x\) increases. This is not present.
• Negative correlation: Requires \(y\) to generally decrease as \(x\) increases. This is not present.
• No correlation: The points are scattered randomly without a discernible linear trend, which matches our analysis.
• More points are needed: We have 14 points, which is sufficient to observe that no clear correlation exists.

Answer:

• 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. (Correct answer)
• More points are needed to determine the correlation.