Two scatter plots have a positive trend. After drawing a trend line for each, you realize that both scatter plots have exactly the same trend line. Which of the following is false?

A. Both scatter plots have the same correlation coefficient.
B. Both scatter plots represent the same data set.
C. The trend line has the same slope for both scatter plots.
D. The relationship between the variables in both scatter plots is linear.

Question

07-08-2024
Mathematics

College

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Two scatter plots have a positive trend. After drawing a trend line for each, you realize that both scatter plots have exactly the same trend line. Which of the following is false?

A. Both scatter plots have the same correlation coefficient.
B. Both scatter plots represent the same data set.
C. The trend line has the same slope for both scatter plots.
D. The relationship between the variables in both scatter plots is linear.

Answer :

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AngusHector AngusHector · Answer 1 · 2025-02-20T07:10:31-05:00

Final answer:

Though two scatter plots may share the same trend line, indicating a similar linear relationship between their respective variables, it doesn't necessarily mean measurements are drawn from the same pair of individuals/objects, or that two sample means are compared.

Explanation:

If two scatter plots have exactly the same trend line, it suggests that the relationship between the X and Y variables in both plots is identical. This means that both plots exhibit a positive trend, which indicates an increase in Y as X increases. This trend can be represented by a trend line in a scatter plot which roughly follows and summarizes the pattern of the scattered points.

However, based on the options provided in the question, answer choice 'D. Answer choices b and c are both true' is false. Even if two scatter plots have the same trend line, it doesn't imply that 'Two measurements are drawn from the same pair of individuals or objects' or that 'Two sample means are compared to each other.' These are separate statistical evaluations that may not be relevant to the scatter plot or trend line at hand.

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