The tables below show four sets of data:
Set A
x
1
2
3
4
5
6
7
8
9
y
10
9
8
7
6
5
4
3
2
Set B
x
1
2
3
4
5
6
7
8
9
y
3
4
5
6
7
8
9
10
11
Set C
x
1
2
3
4
5
6
7
8
9
y
8
6
5
4
3.5
3
2.5
2
2
Set D
x
1
2
3
4
5
6
7
8
9
y
1
2.5
2.5
3
4
5
6
8
9
For which set of data will the scatter plot represent a negative nonlinear association between x and y? (1 point)
Set A
Set B
Set C
Set D
Set A
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To determine which set of data will represent a negative nonlinear association between x and y, we need to analyze the scatter plots for each set.
A scatter plot is a graphical representation of the relationship between two variables. It consists of multiple points plotted on a graph, where each point represents a specific value of x and y.
In a negative nonlinear association, as the value of x increases, the value of y decreases, but the decrease is not constant. This means that the data points will generally lie above a curve or exhibit a pattern that shows a decreasing trend as x increases.
Let's examine each set of data:
Set A:
x: 1 2 3 4 5 6 7 8 9
y: 10 9 8 7 6 5 4 3 2
Set A represents a negative linear association. As x increases, y consistently decreases, forming a straight line. Since the question asks for a negative nonlinear association, we can eliminate Set A.
Set B:
x: 1 2 3 4 5 6 7 8 9
y: 3 4 5 6 7 8 9 10 11
Set B does not exhibit a negative association between x and y. As x increases, y consistently increases. Therefore, we can eliminate Set B as well.
Set C:
x: 1 2 3 4 5 6 7 8 9
y: 8 6 5 4 3.5 3 2.5 2 2
Set C shows a negative nonlinear association between x and y. As x increases, y decreases, but the decrease is not constant. The points do not form a straight line, indicating a nonlinear relationship.
Set D:
x: 1 2 3 4 5 6 7 8 9
y: 1 2.5 2.5 3 4 5 6 8 9
Set D also displays a negative nonlinear association. As x increases, y initially increases before decreasing. The relationship is not linear, and the data points do not form a straight line.
Therefore, the correct answer is Set C.