Question

Which of these correlation numbers shows the strongest relationship?
(a)$+.46$
(b) $+.32$
(c) $-0.41$
(d) $-0.48$

Answer 1

Hint: The correlation coefficient shows the relation between two variables. The absolute value and the sign if the correlation coefficient describes the magnitude and the direction of relationship. Its value lies from -1 to 1. The greater the absolute value of a correlation coefficient, the stronger is the relationship between the variables.

Complete step-by-step solution:
A positive coefficient correlation means that there is a direct relation between the two variables i.e, if the magnitude of one variable increases, then the magnitude of another variable will also increase. While a negative sign shows that there is an inverse relation between the two variables.
To measure the strength of the relationship, we are going to compare the absolute value of the correlation coefficients.
Considering the absolute values of the correlation coefficients, we have
$\begin{align}
  & +.46\Rightarrow 0.46 \\
 & +.32\Rightarrow 0.32 \\
 & -0.41\Rightarrow 0.41 \\
 & -0.48\Rightarrow 0.48 \\
\end{align}$
Now we will arrange the absolute values of the correlation coefficients in decreasing order of arrangement to compare the values,
$0.48>0.46>0.41>0.32$
On arranging these values in decreasing order, we can see the largest value among these is $0.48 $. So, the strongest correlation number will be the one having a value of $0.48$.
So, according to the question,
The correlation number $-0.48$ shows the strongest relationship.

Note: Here, you need to take care of the signs while comparing the correlation coefficients. It should be noted that only the absolute value is compared, not the actual value to analyze the correlation coefficients.
Another thing to note that none of the value here is the strongest correlation coefficient because the strongest correlation coefficients are only -1 and 1. While the weakest correlation coefficient is 0. Here, the value $-0.48$ is a stronger correlation coefficient than the other three that is why it has been termed as the strongest. So, the degree of strength measured here is on relative terms.