Question

1. the correlation coefficients calculated from the data sets used to construct the scatterplots are listed below. select the correlation coefficient that best matches the relationship displayed in each scatterplot.

correlation coefficients: -0.96, 0.14, -0.07, 0.80
scatterplots labeled a, b, c, d (with respective scatter plots shown)

Explanation:

Step1: Analyze Scatterplot a

Scatterplot a shows a negative trend (as x increases, y decreases) with moderate to strong clustering. The correlation coefficient -0.96 is strong negative, but let's check others. Wait, no—wait, let's check each plot:

- Scatterplot a: Points show a negative association, somewhat clustered. Wait, no, maybe I misread. Wait, the y-axis for a: let's see, x and y. Wait, the correlation coefficients given are -0.96, 0.14, -0.07, 0.80.

Step2: Analyze Scatterplot b

Scatterplot b: Points form a strong positive linear trend (close to a line, upward as x increases). So this should have a high positive correlation, like 0.80? Wait, no, 0.96? Wait, no, 0.80 is positive. Wait, the options: -0.96 (strong negative), 0.14 (weak positive), -0.07 (weak negative), 0.80 (strong positive).

Scatterplot b: clear positive linear trend, so correlation around 0.80? Wait, no, maybe 0.96? Wait, no, let's check each:

- Scatterplot a: negative trend, maybe -0.96? Wait, no, the points in a: let's see, x increases, y decreases, and points are somewhat clustered but not super tight. Wait, maybe:

Scatterplot a: negative, moderate? No, -0.96 is strong. Wait, maybe:

Scatterplot b: strong positive, so 0.80? Wait, no, 0.96 is stronger. Wait, maybe the labels:

Wait, the problem is to match each scatterplot (a, b, c, d) with the correlation coefficients (-0.96, 0.14, -0.07, 0.80). Let's re-express:

- Scatterplot b: points form a clear upward linear trend, so high positive correlation. So 0.80 or 0.96? Wait, 0.80 is positive, strong. 0.96 is very strong. If the points are close to a line, 0.96, but maybe 0.80. Wait, maybe:

Scatterplot a: negative trend, points somewhat spread but with a negative slope. So -0.96? No, maybe -0.96 is too strong. Wait, maybe:

Scatterplot c: weak correlation, maybe -0.07 (weak negative) or 0.14 (weak positive). Scatterplot d: weak positive? Wait, no.

Wait, let's do each:

1. Scatterplot a: negative association, moderate to strong? Let's say -0.96 (strong negative).
2. Scatterplot b: positive association, strong (close to a line), so 0.80? Wait, no, 0.96 is stronger. Wait, maybe the given coefficients: -0.96, 0.14, -0.07, 0.80.

Wait, maybe:

- Scatterplot b: strong positive, so 0.80 (since 0.96 is very strong, but maybe the plot is 0.80).
- Scatterplot a: strong negative, -0.96.
- Scatterplot c: weak negative, -0.07.
- Scatterplot d: weak positive, 0.14.

Wait, but the question is to select the correlation coefficient for each? Wait, the original question: "Select the correlation coefficient that best matches the relationship displayed in each scatterplot." Wait, maybe the user is asking for one? Wait, the image shows four scatterplots (a, b, c, d) and four coefficients: -0.96, 0.14, -0.07, 0.80.

Assuming the question is, for example, which coefficient matches scatterplot b (the one with positive trend). Let's focus on scatterplot b: it has a clear positive linear relationship, so the correlation should be positive and strong. Among the options, 0.80 is positive and strong (0.14 is weak, -0.07 and -0.96 are negative). So 0.80? Wait, no, 0.96 is stronger, but maybe the plot is 0.80. Wait, maybe the correct match for scatterplot b is 0.80? Wait, no, let's check again.

Wait, the scatterplot b: points are tightly clustered around an upward line, so correlation close to 1, so 0.80 or 0.96. But the given coefficients: 0.80 is there. So maybe 0.80. Wait, but maybe the answer is 0.80 for scatterplot b.

Wait, maybe the user's question is about one of them. Let's assume the scatterplot in question is b (the middle one with positive trend). So the correlation coefficient is 0.80? Wait, no, 0.14 is weak, -0.07 weak negative, -0.96 strong negative. So positive, strong: 0.80.

Answer:

For scatterplot b (the one with positive linear trend), the correlation coefficient is 0.80. (If the question is about a specific plot, but based on the image, scatterplot b has a strong positive trend, so the best match is 0.80.)