Wyatt wants to study the relationship between the number of siblings that a student has and the student’s grade-point average using a scatterplot. He believes that if the points form a straight line, then there is a relationship between the two variables. Which scatterplot proves that Wyatt’s statement is not always true?

Question

Wyatt wants to study the relationship between the number of siblings that a student has and the student’s grade-point average using a scatterplot. He believes that if the points form a straight line, then there is a relationship between the two variables. Which scatterplot proves that Wyatt’s statement is not always true?
A graph titled Number of Siblings versus Grade-Point Average has Number of Siblings on the x-axis and Grade-point average on the y-axis. Points are at (1, 4), (2, 3), (3, 2), (4, 1).
A graph titled Number of Siblings versus Grade-Point Average has Number of Siblings on the x-axis and Grade-point average on the y-axis. Points are at (1, 3), (2, 3), (3, 3), (4, 3).
A graph titled Number of Siblings versus Grade-Point Average has Number of Siblings on the x-axis and Grade-point average on the y-axis. Points are at (1, 4), (2, 3), (3, 4), and (4, 3).
A graph titled Number of Siblings versus Grade-Point Average has Number of Siblings on the x-axis and Grade-point average on the y-axis. Points are at (1, 1), (2, 2), (3, 3), (4, 4).

GPT-4o mini · Answer

To evaluate Wyatt's statement that points forming a straight line indicate a relationship between the number of siblings and GPA, we need to identify which scatterplot does not form a straight line, suggesting that there is no consistent relationship between the two variables.

First scatterplot (Points: (1, 4), (2, 3), (3, 2), (4, 1)): This forms a straight line with a negative slope.
Second scatterplot (Points: (1, 3), (2, 3), (3, 3), (4, 3)): This forms a horizontal line. All points have the same GPA despite the number of siblings changing, suggesting no relationship.
Third scatterplot (Points: (1, 4), (2, 3), (3, 4), (4, 3)): This does not form a straight line and instead fluctuates, indicating a more complex relationship.
Fourth scatterplot (Points: (1, 1), (2, 2), (3, 3), (4, 4)): This forms a straight line with a positive slope, indicating a positive relationship.

The scatterplot that proves Wyatt's statement is not always true is the second scatterplot, where the GPA remains constant regardless of the number of siblings.