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

Warm-Up: Reading the Correlation Scale

These problems review how to read a given r value.

A regression line has slope $12$ (dollars per hour) and the fit has correlation coefficient $r = 0.6$ . A student says "the correlation is 12." What is the correct value and meaning of $r$ here?

The correlation is $r = 0.6$ , a unitless measure of fit strength on $-1$ to $+1$ ; the slope $12$ is a separate rate with units.

The correlation is $12$ , the same as the slope.

The correlation is $12$ dollars per hour.

The correlation is $0.6$ dollars per hour.