Video Transcript
Which of the following correlation
coefficients indicates the weakest inverse correlation? Is it option (A) negative 0.48,
option (B) negative 0.22, option (C) negative 0.75, or option (D) negative 0.83?
We’re given four correlation
coefficients, and we want to determine which of these indicates the weakest inverse
correlation. We know that Pearson’s correlation
coefficient takes values between negative one and positive one. And we know that if the value is
between negative one and zero, then we have inverse or negative correlation. So all of the given options
represent an inverse relationship. If the coefficient is between zero
and positive one, then our correlation is positive or direct. We also know that the closer the
coefficient is to positive or negative one, the stronger the correlation and that
the closer the coefficient is to zero, the weaker the correlation. And what this means is that the
greater the magnitude of the correlation coefficient, the stronger the
correlation.
So now, if we look at the
magnitudes of our four options, then the magnitude, that is, the absolute value, of
option (A) is 0.48. The magnitude of option (B) is
0.22. The magnitude of options (C) is
0.75. And the magnitude of option (D) is
0.83. Remember, we’re looking for the
correlation coefficient that indicates the weakest correlation. This means the correlation
coefficient with the smallest magnitude, that is, whose magnitude is closest to
zero. We see that our option (B) has a
magnitude closest to zero, and this indicates that (B) represents the weakest
correlation. Our answer is therefore (B) with a
value of negative 0.22.
