Question

On another test, a scientist is looking at the relationship between smoking patterns and pain levels of the patients. He calculated a Pearson's correlation coefficient r to equal .3. What conclusion can be drawn from this finding?

  

a)9% of the variability in smoking patterns can be attributed to the patients' pain levels.

  

b)The correlation between smoking patterns and pain levels is not significant.

  

c)30% of the variability in smoking patterns can be attributed to the patients' pain levels .

  

d)Smoking causes less pain for the patients.

Answer 1

A scientist is looking at the relationship between smoking patterns and pain levels of the patients.

The correlation coefficient r=0.3.

This means r-squared=0.09.

0.09*100=9%

Now, r=0.3; whether it is significant or not, can only be decided from the sample size, of which there is no mention here.

Now, we know that, r-squared is actually the coefficient of determination, which is defined as the percentage of variability in predicted variavle, explained by regression.

So, the correct conclusion is option (a) % of the variability in smoking patterns can be attributed to the patients' pain levels.