Use the table to create scatter plots and determine which scatterplot shows a linear association

Question

A) x- 5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2
y- 12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0
B) x- 5.0, 4.6, 8.5, 7.8, 6.5, 6.8, 7.0, 7.2
y- 3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7
C) x- 5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2
y- 9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5
D) x- 5.0, 4.6, 8.5, 5.9, 7.8, 5.3 7.0, 7.2
y- 12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0

Answer 1

To determine which scatterplot shows a linear association, we can plot each pair of x and y values on a graph.

A) Scatter plot for the first set of values:
x- 5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2
y- 12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0

Based on this scatter plot, it does not show a linear association.

B) Scatter plot for the second set of values:
x- 5.0, 4.6, 8.5, 7.8, 6.5, 6.8, 7.0, 7.2
y- 3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7

This scatter plot also does not show a linear association.

C) Scatter plot for the third set of values:
x- 5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2
y- 9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5

This scatter plot does not show a linear association.

D) Scatter plot for the fourth set of values:
x- 5.0, 4.6, 8.5, 5.9, 7.8, 5.3, 7.0, 7.2
y- 12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0

Based on this scatter plot, it shows a linear association as the points seem to follow a linear trend.

Therefore, the scatter plot that shows a linear association is Option D.