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Suppose you see a scatter plot where the dots follow a general straight-line increasing trend. The x-axis is labeled with equally spaced numbers 1, 10, 100, 1000, 10000, and the y-axis is labeled using equally spaced numbers 10, 20, 30, 40, 50.

What is a way that we can explain the relationship between x and the average value of Y?

A. An absolute increase in X corresponds with an absolute increase in the average value of Y.
B. An absolute increase in X corresponds with a percentage increase in the average value of Y.
C. A percentage increase in X corresponds with an absolute increase in the average value of Y.
D. A percentage increase in X corresponds with a percentage increase in the average value of Y.

Answer :

Final Answer:

An absolute increase in X corresponds with a percentage increase in the average value of Y, Option b is correct.

Explanation:

The relationship between X and the average value of Y can be explained by option B, where an absolute increase in X corresponds with a percentage increase in the average value of Y.

In this scatter plot, both X and Y axes have logarithmically spaced labels. When X increases from 1 to 10, it represents a tenfold increase. However, the Y-axis remains equally spaced, indicating that each increment on the Y-axis represents a fixed percentage change.

As X increases, the dots following a straight-line increasing trend suggest a proportional increase in Y. This means that for every unit increase in X, Y increases by a certain percentage. Therefore, option B accurately describes this relationship, where an absolute increase in X (e.g., from 1 to 10) corresponds with a percentage increase in the average value of Y, maintaining the linear trend seen in the scatter plot.

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