### 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, or (B) a moderate negative linear correlation, or (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 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 of positive 0.8. And the correlation coefficient of
positive 0.8 means that we have direct or positive correlation. And noting that the product-moment
correlation coefficient applies to linear correlation, we can eliminate any of our
options, which interpret the coefficient as a negative linear correlation.

This means we can eliminate option
(A) and option (B) since these both specify negative linear correlation. We can also eliminate option (E)
since this specifies no correlation and we do not have zero correlation. This leaves us with option (C) and
option (D), a moderate positive linear correlation or a strong positive linear
correlation. If we consider the magnitude of
correlation coefficients — the stronger the correlation, the closer the magnitude to
positive or negative one. The closer the magnitude is to
zero, the weaker the correlation — then this means 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 say this represents strong positive linear
correlation. We can therefore eliminate option
(C), which refers to a moderate positive linear correlation. And so the most appropriate
interpretation of a product-moment correlation coefficient of 0.8 is option (D) a
strong positive linear correlation.