Question

The formula of product moment correlation is ____________.
A.\[r = \dfrac{{{S_{xy}}}}{{\sqrt {{S_x}{S_y}} }}:S = {\text{Standard error}}\]
B.\[r = \dfrac{{{\sigma _{xy}}}}{{N{\sigma _x}{\sigma _y}}}:N = {\text{Number of variables}}\]
C.\[r = \dfrac{{ - {r^2}}}{{\sqrt N }}\]
D.\[r = \dfrac{{6{\sigma _d}^2}}{{n\left( {{n^2} - 1} \right)}}\]

Answer 1

Hint: First we will use Karl pearson's coefficient of correlation to determine how strongly the two variables are related to each other i.e. measure the linear correlation between the variables to find the required value.

Complete step-by-step answer:
We are given the product moment correlation.
Let us assume that the standard error is \[S\].
We know that the formula for product moment correlation given in the option A is correct and measures the linear relationship between two variables.
As we know that the formula basically tries to show how strong are the two variables, we have \[x\] and \[y\] in this case, which are related to each other. A correlation could be weakly or strongly correlated depending on the value of \[r\].
So we know that Karl pearson's coefficient of correlation determines how strongly the two variables are related to each other i.e. measure the linear correlation between the variables.
Therefore, the required value is \[r = \dfrac{{{S_{xy}}}}{{\sqrt {{S_x}{S_y}} }}:S = {\text{Standard error}}\].
Hence, option A is correct.

Note: We need to know that the correlation refers to the degree of correspondence or relationship between two variables. Correlated variables tend to change together. If one variable gets larger, the other one systematically becomes either larger or smaller. For example, we would expect to find such a relationship between scores on an arithmetic test taken three months apart. We could expect high scores on the first test to predict high scores on the second test, and low scores on the first test to predict low scores on the second test.