Question

Assuming the coefficient of determination for a correlational study is 23%, explain (30 words or less) whether the interpretation is correct or not.

Twenty three percent of the variability in body weight can be accounted for by the number of hours slept per night. This is a large effect, indicating that the two variables are strongly correlated with each other.

Answer 1

There are two statements made here. The coefficient of determination is defined as the proportion of variability in the dependent variable that is explained by the independent variable. Therefore Twenty three percent of the variability in body weight can be accounted for by the number of hours slept per night, that is the first statement is absolutely correct here. Therefore the first statement is correct here.

The correlation coefficient between the two variables is defined as the square root of coefficient of determination. Therefore here it is computed as:

As the correlation coefficient here is not very high ( close to 1 is a positive strong correlation ), therefore the two variables are actually very weakly correlated. Therefore the second statement is False here.