Question

Consider the following sample data:

x 21 22 25 28 24

y 15 22 26 28 29

a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b. Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Answer 1

x	y	X*Y	X2	Y2
21.00	15.00	315.00	441.00	225.00
22.00	22.00	484.00	484.00	484.00
25.00	26.00	650.00	625.00	676.00
28.00	28.00	784.00	784.00	784.00
24.00	29.00	696.00	576.00	841.00
120.00	120.00	2,929.00	2,910.00	3,010.00

Correlation Calculations
	Answer		Answer
n	5.0000	SSxx	30.0000
∑Xi	120.0000	SSyy	130.0000
X bar	24.0000	SSxy	49.0000
∑Yi	120.0000
Y bar	24.0000	Correlation r	0.7846
∑Xi*Yi	2929.0000
X2	2910.0000
Y2	3010.0000

Based on the above table, the following is calculated: a. Now, the covariance between X and Y is computed using the following expression: b. Therefore, based on this information, the sample correlation coefficient is computed as follows:

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