Question

What is the approximate value of the correlation coefficient for the given graph?

Answer 1

Answer:

-1.

Step-by-step explanation:

The graph decreases by 5 for every year, so it has a perfect linear dependence of |1|. The graph is also negative, so the correlation coefficient has to be negative.

Answer 2

Answer:

-1

Step-by-step explanation:

The Correlation Coefficient is defined to measure the strength of the relationship between two variables. Different kinds of correlation coefficient exist, each with has their description and own limit of usability and components Value of Correlation Coefficient always lies within -1 to +1.

If Correlation Coefficient has a value -1 then it has an absolute negative correlation, while if the correlation coefficient has a value of +1 it shows an absolute positive correlation. A correlation of value 0.0 shows there is no correlation between the movements of the two variables.

The Correlation coefficient is measured by the Scatter plot or by Pearson Correlation Coefficient. In the Scatter Plot, we plot the graph between these two variables. If both variables are either increases or decrease then there is a Positive Correlation, and its value is positive that is greater than 0 but less or equal to 1 but if one variable increases and other decreases or vice- versa then there is a Negative Correlation and its value is less than zero but greater than or equal to -1. If the value of Correlation coefficient is less than -1 and greater than +1 then we possibly do mistake in calculating values.

The Pearson Correlation coefficient is determined by the covariance of both the variables divided by the product of standard deviation of the given variable.

It is represented by greek letter rho(ρ)

$\rho_{(X,Y)}=\frac{Cov(X,Y)}{\sigma_X\sigma_Y}$

where,

cov= covariance of variables X and Y

$\sigma_X$ = standard deviation of X

$\sigma_Y$ = standard deviation of Y.

The formula of the Pearson Correlation Coefficient can also be expressed in mean and expectation which is given by,

$\rho_{(X,Y)}=\frac{E(X-\mu _X)(Y-\mu_Y)}{\sigma_X\sigma_Y}$

where,

$\mu_X$ = mean of X

$\mu_Y$ = mean of Y

E = Expectation.

Here the given graph is a strong negative linear relationship type. It has a perfect negative correlation.

Here, Option A. is incorrect because it is use for strong positive linear relationship

Option B. and C. is not a possible value for Correlation Coefficient.

Therefore, Option D. is correct.

That is, Correlation Coefficient ( r ) is equal to -1.

When one variable increases and other variable decreases, a negative linear relationship exists.