Question

does the scatter plot show a positive, negative, or no correlation? explain
determine whether this data illustrates correlation or causation.

Explanation:

Step1: Analyze the scatter - plot trend

In a scatter - plot, if as one variable (x - axis: blueberries) increases, the other variable (y - axis: strawberries) also increases, it shows a positive correlation. Looking at the points: when the amount of blueberries (x - values) goes from a lower value (say \(x = 4\)) to a higher value (\(x=6\)), the amount of strawberries (y - values) goes from \(y = 14\) (when \(x = 4\)) to \(y=8\) (when \(x = 6\)) following an increasing trend.

Step2: Define correlation types

• Positive correlation: \(y\) - values increase as \(x\) - values increase.
• Negative correlation: \(y\) - values decrease as \(x\) - values increase.
• No correlation: There is no discernible pattern between \(x\) and \(y\) values.

Since the points in the scatter - plot show that as the number of pounds of blueberries (x) increases, the number of pounds of strawberries (y) decreases, we can rule out negative and no correlation.

Step3: Check for causation

Causation means that a change in one variable directly causes a change in another variable. Just because there is a positive correlation (an association) between the number of pounds of blueberries and strawberries in a scatter - plot, we cannot say that one causes the other. There could be other factors (e.g., a person's overall fruit - buying budget, a store's fruit availability) that influence both quantities.

Answer:

The scatter - plot shows a positive correlation. Correlation implies a relationship (as blueberries increase, strawberries increase), but there is no causation. We cannot say that an increase in blueberries directly causes an increase in strawberries. There could be other external factors affecting the amounts of both fruits.