Match Scatter Plots to Correlation Coefficients Statistics Practice Problem

Question

Match each scatter plot graph (a, b, c, d, e, f) to the corresponding correlation coefficient: R = -0.85, R = -0.3, R = 0.3, R = -1, R = 0.85, R = 1.

Accepted Answer

Graph (a) → R = 1; Graph (b) → R = 0.85; Graph (c) → R = 0.3; Graph (d) → R = -1; Graph (e) → R = -0.85; Graph (f) → R = -0.3

Answer

Step 1: Recall that the correlation coefficient R ranges from -1 to 1. A value of 1 means a perfect positive linear relationship, -1 means a perfect negative linear relationship, values close to 0 mean no linear relationship, and values between 0 and 1/-1 mean a weak or strong positive/negative linear relationship. Step 2: Identify perfect linear relationships: Graph (a) has points in a perfect positive straight line, so it matches R = 1. Graph (d) has points in a perfect negative straight line, so it matches R = -1. Step 3: Identify strong positive/negative relationships: Graph (b) has a strong positive linear trend (points clustered tightly around a positive line), so it matches R = 0.85. Graph (e) has a strong negative linear trend (points clustered tightly around a negative line), so it matches R = -0.85. Step 4: Identify weak positive/negative relationships: Graph (c) has a weak positive linear trend (points loosely scattered around a positive line), so it matches R = 0.3. Graph (f) has a weak negative linear trend (points loosely scattered around a negative line), so it matches R = -0.3.