Question

Consider the following sample data for two variables. IC x 4 2 2 16 y 9 10 16 5 311 a. Calculate the sample covariance b. Calculate the sample correlation coefficient. c. Describe the relationship between x and y ell 1( a. S xy Round to two decimal places as needed) hi

Answer 1

a. The sample covariance ,

Using excel function,we calculate

Sxy =∑_i  (Xi-xbar) * (Yi-ybar) /n-1 (for sample covariance)

where xbar =average of the x; ybar =average of y and n=4

Sxy=SUM(F3:F6)/3=-24

(A negative value of sample covariance indicates the variables x and y move in inverse directions)

b. Correlation coefficient =r =CORREL(B3:B6,C3:C6)=-0.784

The value of r indicates that there is a strong inverse relationship between x and y.

c.Both the correlation and covariance values indicate that there is inverse relationship between x and y.

i.e X increases if y decreases and viceversa.

Calculations are as shown below :

fCORREL(B3:B6,C3:C6) В 10 (Xi-xbar) Xi-xbar Yi-ybar Yi-ybar 2 Sample X 2 4 2 2 16 10 16 24 10 4 10 7 Mean 24 9 Covariance 0.784 10 Correlation