Calculate the correlation coefficient for the following data: X=0, -1, -2, -3, -2, -2, 0, 1,...

Calculate the correlation coefficient for the following data:

X=0, -1, -2, -3, -2, -2, 0, 1, 2, 3, 2, 1

Y=3, 2, 1, 0, -1, -2, -3, -2, -1, 0, 1, 2

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Solutions

Expert Solution

Correlation coefficients are used in statistics to measure how strong a relationship is between two variables. There are several types of correlation coefficient: Pearson’s correlation (also called Pearson’s R) is a correlation coefficient commonly used in linear regression.

Formula for Pearson's correlation coefficient is given by

	X	Y	XY	X²	Y²
	0	3	0	0	9
	-1	2	-2	1	4
	-2	1	-2	4	1
	-3	0	0	9	0
	-2	-1	2	4	1
	-2	-2	4	4	4
	0	-3	0	0	9
	1	-2	-2	1	4
	2	-1	-2	4	1
	3	0	0	9	0
	2	1	2	4	1
	1	2	2	1	4
Sum	-1	0	2	41	38

Now

In excel, you can use

=CORREL(array1,array2)

Therefore, the correlation coefficient between two variable is 0.05

orchestra answered 1 year ago

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Subjects

	X	Y	XY	X²	Y²
	0	3	0	0	9
	-1	2	-2	1	4
	-2	1	-2	4	1
	-3	0	0	9	0
	-2	-1	2	4	1
	-2	-2	4	4	4
	0	-3	0	0	9
	1	-2	-2	1	4
	2	-1	-2	4	1
	3	0	0	9	0
	2	1	2	4	1
	1	2	2	1	4
Sum	-1	0	2	41	38

	X	Y	XY	X²	Y²
	0	3	0	0	9
	-1	2	-2	1	4
	-2	1	-2	4	1
	-3	0	0	9	0
	-2	-1	2	4	1
	-2	-2	4	4	4
	0	-3	0	0	9
	1	-2	-2	1	4
	2	-1	-2	4	1
	3	0	0	9	0
	2	1	2	4	1
	1	2	2	1	4
Sum	-1	0	2	41	38

	X	Y	XY	X²	Y²
	0	3	0	0	9
	-1	2	-2	1	4
	-2	1	-2	4	1
	-3	0	0	9	0
	-2	-1	2	4	1
	-2	-2	4	4	4
	0	-3	0	0	9
	1	-2	-2	1	4
	2	-1	-2	4	1
	3	0	0	9	0
	2	1	2	4	1
	1	2	2	1	4
Sum	-1	0	2	41	38