Question Type 5: Describing the correlation Exercises

Two variables have a correlation coefficient of $r = -0.30$. Describe what this tells you about the relationship and whether you would consider it strong.

The scatter diagram below shows points closely clustered around a downward-sloping line. Describe the correlation.

A dataset has a calculated correlation coefficient $r = -0.62$. Describe the strength and direction of the correlation.

Given a scatter diagram with correlation coefficient $r = 0.85$, describe the strength and direction of the correlation.

Given $r = -0.95$ for two variables, calculate the coefficient of determination and describe the correlation strength and direction.

A scatter plot of annual rainfall vs. crop yield shows points tightly clustered along an upward line but with one outlier far below the line. Describe how the outlier affects the correlation coefficient.

A scatter diagram shows a weak positive correlation. Suggest a plausible value for the correlation coefficient $r$ and justify your answer.

Dataset A has $r_A = 0.8$ and dataset B has $r_B = -0.8$. Compare their correlations in terms of strength and direction.

Interpret a correlation coefficient of $r = 0$. What does this tell you about the relationship between the two variables?

A researcher reports $r = 0.15$ between hours studied and test scores. Describe this correlation.

Explain the difference between a correlation coefficient of $r = 0.7$ and a coefficient of determination $r^2 = 0.7$.

In a study, the coefficient of determination between study time and exam score is $r^2 = 0.49$. Describe what this implies about the strength of the linear relationship.