To analyze the scatterplots for linear association based on the provided data sets, we will look at the coordinates (x, y) given in each instance.
Here they are summarized for clarity:
-
First Set:
- (5, 800)
- (8, 700)
- (2, 350)
- (4, 450)
- (6, 500)
- (12, 1000)
- (10, 900)
- (1, 400)
- (3, 750)
-
Second Set:
- (5, 800)
- (8, 700)
- (2, 350)
- (4, 450)
- (6, 500)
- (12, 1000)
- (10, 900)
- (1, 400)
- (3, 750)
-
Third Set:
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 500)
- (6, 500)
- (12, 400)
- (10, 650)
- (1, 150)
- (3, 400)
-
Fourth Set:
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 500)
- (6, 500)
- (12, 400)
- (10, 650)
- (1, 150)
- (3, 400)
-
Fifth Set:
- (5, 550)
- (8, 800)
- (2, 250)
- (4, 300)
- (6, 700)
- (12, 1000)
- (10, 650)
- (1, 300)
- (3, 100)
-
Sixth Set:
- (5, 550)
- (8, 800)
- (2, 350)
- (4, 450)
- (6, 700)
- (12, 1000)
- (10, 900)
- (1, 250)
- (3, 400)
- (7, 750)
To assess which scatterplot might show a linear association, we look for a consistent pattern where the y-values increase or decrease steadily with the x-values.
- First Set and Second Set both seem to follow a somewhat linear trend but have some deviations.
- Third Set and Fourth Set show more variance in the y-values, suggesting a weaker association.
- Fifth Set has a more scattered distribution around the y-axis, making it less likely to show linear association.
- Sixth Set has some linear aspects but also shows scatter.
Based on these observations, the first and second sets most closely approximate a linear relationship, though it is important to plot them visually for confirmation. Hence, while both may indicate some potential for linearity, we can conclude the first set shows the strongest linear association.
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