Question

Find the covariance and correlation coefficient for the following sets of data. Select the answers equal to or closest to your results. X: 50 44 47 40 54 Y: 10 13 95 7 Cov What does each measure tell you? Check all that apply. The covariance tells you that there is a weak or nonexistent linear relationship between X and Y The covariance and correlation coefficient tell you that there is a positive linear relationship between X and Y. The correlation coefficient tells you that there is a negative linear relationship between X and Y □ The correlation coefficient tells you that there is a strong linear relationship between X and Y □ The correlation coefficient tells you that there is a weak or nonexistent linear relationship between X and Y. What don't these measures tell you? Check all that apply. If you observe a larger value of X, you are likely to see a larger value of Y associated with it. If you change the value of X, you will make the value of Y become smaller. A larger value of X causes the value of Y to be larger. If you change the value of X, you wl make the value of Y become larger.

Answer 1

Answer: Cov= 1.25

r= 0.0765

Correlation measures tells that there is a weak or non-existence of linear relationship between X and Y as it is very less or less than 0.1.

In second case all of the options are correct, as there is a weak or non-existence of relationships so we can not say anything about X and Y.

Calculation Sum(X) = 50 + 44 + 47 + 40 + 54 = 235 X_Mean = 47 Sum(Y) = 10 + 13 + 9 + 5 + 7 = 44 Y_Mean = 8.8 Covariance (X, Y) = SUM(X_i - X_mean) * (y_i - y_mean)/(samplesize - 1) = (50 - 47)*(10 - 8.8) + (44 - 47)*(13 - 8.8) + (47 - 47)*(9 - 8.8) + (40 - 47)*(5 - 8.8) + (54 - 47)*(7 - 8.8))/4 = 1.25