Back to Compute and interpret the correlation coefficient — Problem 3 · Task Set 10

Exercises: Compute and Interpret the Correlation Coefficient

Work through each section in order. The correlation coefficient r measures the STRENGTH and DIRECTION of a LINEAR association on a scale from -1 to +1. Read its SIGN for direction and its MAGNITUDE (distance from 0) for strength. Where a problem gives a calculator or spreadsheet value, use it as your computed r. Remember: r sees only straight-line patterns, an outlier can swing it, and a high r never proves causation.

Grade 10·21 problems·~30 min·Common Core Math - HS Statistics and Probability·group·hss-id-c-8

Work through problems with immediate feedback

Fluency Practice

Estimate r from each plot, or read and interpret a given r value.

$A scatter plot whose points drift upward overall but spread out loosely around the trend.$

The scatter plot below shows points that drift upward overall but spread out in a loose cloud around the trend. Which value of $r$ best matches this plot, and is the association strong or moderate?

$r \approx 0.5$ — a moderate (loose) positive association.

$r \approx 0.95$ — a strong (tight) positive association.

$r \approx 0.5$ — a strong positive association, since $0.5$ is large.

$r \approx -0.5$ — a moderate negative association.