Problem

Here is a scatter plot for a set of bivariate data. What would you estimate the correlation coefficient to be? \[ \begin{array}{ccccc} -0.9 & -0.6 & 0 & 0.6 & 0.9^{x} \\ 0 & 0 & 0 & 0 & 0 \end{array} \]

Solution

Step 1 :The correlation coefficient, often denoted by r, is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative linear relationship, 1 indicates a strong positive linear relationship, and 0 indicates no linear relationship.

Step 2 :The provided data seems to be a single row of x-values (-0.9, -0.6, 0, 0.6, 0.9) and a single row of y-values (0, 0, 0, 0, 0). This would suggest that there is no variation in the y-values for different x-values, which would mean there is no linear relationship between the two variables.

Step 3 :However, without a proper scatter plot or more context, it's hard to accurately estimate the correlation coefficient.

Step 4 :Since the y-values are all the same, we can calculate the correlation coefficient, which should return NaN (not a number) because the standard deviation of the y-values is zero (they are all the same), and the correlation coefficient formula involves division by the standard deviation of y.

Step 5 :As expected, the correlation coefficient is not a number (NaN) because there is no variation in the y-values, so there is no linear relationship between the x and y variables.

Step 6 :Final Answer: The correlation coefficient is \(\boxed{\text{NaN}}\).

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Source: https://solvelyapp.com/problems/42268/

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