Question

1. a correlation coefficient value of $r = 0.85$ suggests a moderately strong linear association between two variables. however, as demonstrated in the following exercise, a line may not be the best model or representation of the data.

a. produce a scatterplot for the following table of values. how would you describe the association between $x$ and $y$?
(table of $x$ and $y$ values: $x$: 0.5, 0.5, 1, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5, 5.5, 5.5, 6, 6.5, 7, 7, 7.5, 8; $y$: 3.2, 2.9, 2.5, 2.1, 2.6, 1.8, 2.6, 2.2, 3.3, 2.9, 3.1, 3.6, 4, 4.1, 3.1, 3.9, 4.9, 4.6, 5.3, 6.3, 7.4)

Explanation:

Step1: Plot points on scatterplot

Mark (x,y) pairs: (0.5,3.2), (0.5,2.9), (1,2.5), (1,2.1), (1.5,2.6), (2,1.8), (2.5,2.6), (3,2.2), (3.5,3.3), (4,2.9), (4.5,3.1), (5,3.6), (5,4), (5.5,4.1), (5.5,3.1), (6,3.9), (6.5,4.9), (7,4.6), (7,5.3), (7.5,6.3), (8,7.4), (8,6.2).

Step2: Analyze association pattern

Observe points: x from 0.5-3, y fluctuates ~1.8-3.3; x ≥3.5, y increases with x. Overall, positive association, non-linear (fluctuates then rises).

Answer:

There is a positive, non-linear association between x and y (y fluctuates at small x then increases with x).