IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
Which statement about a sample correlation coefficient close to zero is correct?
A correlation near zero means little linear association, but a non-linear relationship can still exist. Correlation measures only linear dependence, so zero correlation does not imply independence.
- AThere is no relationship of any kind between the variables
- BThe variables must be statistically independent
- CThe regression of y on x must have a steep slope
- DThere is little linear association, but a non-linear relationship may existCorrect
- The scatterplot must show points forming a perfect horizontal line only
Explanation
Correlation measures only linear association. For example, y = x² with x symmetric about zero gives r near 0 despite exact dependence. Hence zero correlation does not imply independence.
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