Question

as you answer the questions below, consider how the value of the correlation coefficient relates to the strength of the linear relationship. below are two scatter plots with given lines of best fits and correlation coefficients. why is the correlation coefficient for men’s income lower than for women’s income? use visual trends in both scatter plots to justify your response.

Explanation:

The correlation coefficient measures the strength of linear relationship. For men’s income (left plot), data points are more scattered around the line of best fit, showing less linear association. For women’s income (right plot), points cluster closer to the line, indicating a stronger linear trend. A lower correlation coefficient (0.17 vs 0.88) means weaker linear relationship, which matches the visual scatter: more spread in men’s data reduces the linear association strength.

Answer:

The correlation coefficient for men’s income is lower because the data points in the men’s income scatter plot are more widely scattered around the line of best fit (showing a weaker linear trend), while the women’s income data points cluster more closely to their line of best fit (showing a stronger linear trend). A lower correlation coefficient reflects less linear association, which aligns with the greater scatter in men’s income data.