Answer:
a. Covariance between x and y = – 1.25
b. Correlation coefficient = – 0.07
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Consider the following sample data:
x 10 7 20 15 18
y 22 15 19 14 15
Required:
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The explanation to the answer is now given as follows:
Note: See the attached excel file for the calculations of the sum of x and y, means of x and y, deviations of x and y, multiplications of deviations of x and y, and others.
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
In the attached excel file, we have:
N = Number of observations = 5
Mean of x = Sum of x / N = 70 / 5 = 14
Mean of y = Sum of y / N = 85 / 5 = 17
x - Mean of x = Deviations of x = see the attached excel file for the answer of each observation
y - Mean of y = Deviations of y = see the attached excel file for the answer of each observation
Multiplications of the deviations of x and y = (x - Mean of x) * (y - Mean of y) = see the attached excel file for the answer of each observation
Sum of the multiplications of deviations of x and y = Sum of ((x - Mean of x) * (y - Mean of y)) = –5
Since we are using a sample, we use (N – 1) in our covariance between x and y as follows:
Covariance between x and y = Sum of ((x - Mean of x) * (y - Mean of y)) / (N – 1) = –5 / (5 – 1) = –5 / 4 = –1.25
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The correlation coefficient can be calculated using the following formula:
Correlation coefficient = Covariance between x and y / (Sum of (x - Mean of x)^2 * Sum of (y - Mean of y)^2)^0.5 ………………… (1)
Where, from the attached excel file;
Covariance between x and y = –5
Sum of (x - Mean of x)^2 = 118
Sum of (y - Mean of y)^2 = 46
Substituting the values into equation (1), we have:
Correlation coefficient = –5 / (118 * 46)^0.5 = –5 / 5,428^0.5 = –5 / 73.6750 = – 0.07
