Question

Ch 014: Assignment - Numerical Descriptive Techniques < Back to Assignment Attempts: Average: 17 6. Measures of linear relationship - Covariance and coefficient of correlation Consider a data set consisting of observations for three variables: X, Y, and z. Their sample means, variances, and standard deviations are shown in Table 1 Table 1 Sample Mean 1-3 - 7 2-3 Sample Variance *- 1 - 13 Sample Standard Deviation - 1 - 3.606 - 1.732 Table 2 shows the observations for X and Y and their corresponding deviations from the sample means, Table 2 -- 2 3 -4 3 B 0 1 4 10 3 1 The sample covariance between x and 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 - -2 3 2 -1 8 5 1 2 10 2 3 The sample covariance between y and is The sample correlation coefficient between y and is Table 4 shows the observations for x and z and their corresponding deviations from the sample means Table 1 -1-1 2 2 -1 35 2 -1 The sample covariance between x and is The sample correlation coeficient between x and Select the best conclusion based on your calculations of the preceding correlation concerts The calculation show a strong positive linear relationship between and y, positive ne relationship between y and I, and no linear relationship between x and The calculation show a positive linear relationship between and y, a negative linear relationship between yond and a gative in relationship between and The calculations show a negative linear relationship between x and y. a positive linear relationship between y and, and no relationship between and z. The calculations show a negative relationship between x and positive relationship between Yand and a negative relationship between K and 2. Gradeshow Se & Conde Cornew house

Answer 1

The sample covariance is given by :

n COV(x,y) = (x– x)(); – 5) i=1 n-1

The sample correlation coefficient is given by :

SIY Try Sy and sy are the sample standard deviations, and sxy is the sample covariance.

FOR X AND Y

The sample covariance between x and y =

4+3 —1*4+0+1+1+3 3-1 = = 3.5

The sample correlation coefficient between x and y =

3.5 3.5 0.97 1*3.606 3.606

FOR Y AND Z

The sample covariance between y and z =

4-2-3 -4-1+1+2+3* -1 3-1 - -1.5 2 2

The sample correlation coefficient between y and z =

15 15 0.24 3.606*1.732 6.2456

FOR X AND Z

The sample covariance between x and z =

1+0-1 -1* -1 +0+2+1+ -1 3-1 ||| 2 2

The sample correlation coefficient between x and z =

0 1.732*1 =0

The calculations show strong positive linear relationship between x and y, a positive linear relationship between y and z and no linear relationship between z and x