Question

2. The following sample of observations are given for two variables 12 6 20 3 21 1 19 2 18 3 You are told that the mean for x is 18, the standard deviation for x is 3.535534, and the mean for v is 3. a) Find the standard deviation for y b) Compute and the sample covariance for the above data c) Compute and interpret sign and the size of the sample correlation coefficient

Answer 1

The provided data is, =18 S = 3.535534 J = 3 a) The standard deviation of y is, E (:- 1) s= 1 (6-3)? +(3-3)* +(1-3) +(2-3)? +(3-3)? 5-1 = 1.87083

b) The sample covariance is, y 12 6 x-(x-bar) y-v-bar) (x-(x-bar))*(v-y-bar)) -6 -18 -1 Sum 90 -25 18 3 15 Mean 18 Std Dev 3.53553 1.87083

Cor(x, y) == $(*. - )(– 5) c) The sample correlation coefficient is, Cov(x,y) Corr(x,y)= I sus, -6.25 (3.53553)(1.87083) = -0.9449 The sample correlation is -0.9449 which is close to -1 indicates a strong negative (due to minus sign) relationship between the variables x and y.