(a)
Determine the covariance and coefficient of correlation.
(a)
Explanation of Solution
Covariance is a measure that is used to measure the relationship between the movements of two variables. Thus, covariance measures how changes in one variable are associated with the changes in a second variable. Therefore, covariance measures the degree to which two variables are linearly associated. In this case, covariance can be measured after calculating the square of x and y and the product of xy as follows:
20 | 14 | 400 | 196 | 280 |
40 | 16 | 1600 | 256 | 640 |
60 | 18 | 3600 | 324 | 1080 |
50 | 17 | 2500 | 289 | 850 |
50 | 18 | 2500 | 324 | 900 |
55 | 18 | 3025 | 324 | 990 |
60 | 18 | 3600 | 324 | 1080 |
70 | 20 | 4900 | 400 | 1400 |
Covariance can be calculated as follows:
The values of two standard deviations can be calculated as follows:
Similarly,
The coefficient of determination can be calculated by squaring the coefficient of correlation as follows:
Thus, covariance is calculated to be 26.16 and the coefficient of correlation is calculated to be 0.9711. The coefficient of determination is also calculated, and it is 0.9430. These values indicate that 94.30 percent of variation in variable ‘y’ is explained by the variations in variable ‘x’.
Covariance: Covariance is a measure that is used to measure the relationship between the movements of two variables.
(b)
Determine the least squares line and estimate the retailer wants.
(b)
Explanation of Solution
Covariance is calculated to be 26.16, and the value of
The values of
Similarly,
The value of
The least square line will thus be
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Chapter 4 Solutions
Statistics for Management and Economics (Book Only)
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