Question

In: Statistics and Probability

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

Find through Excel.

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


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