Exercise: Head circumference and height, answer 13

Question 13: How do the significance tests for the correlation coefficient being zero and the regression slope being zero compare? Are their assumptions different?

Suggested answer

The P values are exactly the same. Although the assumptions appear different, they are not really. If the null hypothesis is true, the slope of the line will be zero and the residuals will have the same distribution as the outcome variable, apart from the mean. If the residuals follow a Normal distribution, as required for regression, then the variable itself will follow a Normal distribution, as required for correlation.

Note that the assumptions are the same only for the test of significance, not for confidence intervals, where we do not hypothesise that there is no relationship.

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