14. Measures of association between two variables Consider a data set consisting of observations for three variab'es: x, y, and 2. Their sample means, variances, and standard deviations are shown in Table 1. Table 1 Sample Mean )2 = 3 37 = 3 E = 3 Sample Variance 5x2 = 4 5y? = 1 sf = 3 Sample Standard Deviation s1 = 2 5y = i 52 = 1.732 Table 2 shows the observations for x and y and their corresponding deviations from the sample means. Table 2 Xi yi Xi - X yi - y 3 -2 0 3 2 0 - 1 UT 4 2 The sample covariance between x and y is The sample correlation coefficient between x and y is Table 3 shows the observations for y and z and their corresponding deviations from the sample means.Table 3 yi Zi yi - y Zi - Z 4 0 2 -1 -2 4 4 The sample covariance between y and z is The sample correlation coefficient between y and z is Table 4 shows the observations for x and z and their corresponding deviations from the sample means.1 4 -2 1 3 1 0 -2 5 4 2 1 The sample covariance between x and z is The sample correlation coefficient between x and z is Select the best conclusion based on your calculations of the preceding correlation coefficients. 0 The calculations show a negative relationship between x and y, a positive relationship between V and z, and a negative relationship between x and z. O The calculations show a positive linear relationship between x and y, a negative linear relationship between y and z, and a negative linear relationship between x and 2. O The calculations show a negative linear relationship between x and y, a positive linear relationship between y and z, and no relationship between x and z. O The calculations show a positive linear relationship between x and y, a positive linear relationship between V and z, and no linear relationship between x and z