Question

A recent study reported a finding that heavy alcohol consumption was correlated with an increased risk of developing lung cancer. Respond to each of the prompts below.

A) If you were to calculate a correlational coefficient for these two variables and it turned out to be .5 how would you interpret this relationship? I.e., what is the relationship between the two variables?

B) How would you interpret the coefficient of determination for the outcome described above where the r value was determined to be .5? What is the importance of this result?

Answer 1

(A) Correlation coefficient is r = 0.5

this value is positive, which means that there is positive and weak linear relationship between independent and dependent variables

so, we can say that increase in independent variable will show increase in the dependent variable

(B) Coefficient of determination = r^2

where r = 0.5

so, we get

coefficient of determination = 0.5^2

= 0.25

or 0.25*100 = 25%

So, only 25% variation in the dependent variable can be explained by the independent variable. This is very low explained variation, this suggets that model is not good