### Video Transcript

Which of the following is the most
appropriate interpretation of a product-moment correlation coefficient of 0.8? Is it (A) a strong negative linear
correlation, (B) a moderate negative linear correlation, (C) a moderate positive
linear correlation, (D) a strong positive linear correlation, or (E) no
correlation?

We know that Pearson’s
product-moment correlation coefficient 𝑟 subscript 𝑥𝑦 or just 𝑟 takes values
between negative one and positive one. We also know that if 𝑟 is less
than zero and greater than or equal to negative one, then we have inverse or
negative correlation and that if 𝑟 is greater than zero and less than or equal to
positive one, we have direct or positive correlation. We’re asked which of the given
options is the most appropriate interpretation of a product-moment correlation
coefficient with a value of 0.8. Since this value is positive, we
know that we have direct or positive correlation. This means we can eliminate any of
our options that specify negative correlation. So we can eliminate options (A) and
(B), since these both specify a negative correlation. We can also eliminate option (E),
since no correlation would give us a correlation coefficient of zero. And our correlation coefficient is
nonzero; it’s 0.8.

This leaves us with options (C) and
(D), a moderate positive linear correlation or a strong positive linear
correlation. If we consider the magnitude of the
correlation coefficient, the stronger the correlation, the closer the magnitude to
one. And the closer the magnitude is to
zero, the weaker the correlation. This means then that approximately
midway between zero and positive or negative one, we have moderate correlation. Since the given coefficient is 0.8,
which is close to positive one, we can therefore say that this represents strong
positive correlation. And so the most appropriate
interpretation of a product-moment correlation coefficient of 0.8 is option (D), a
strong positive linear correlation.