(a)
Determine the covariance.
(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:
40 | 77 | 1600 | 5929 | 3080 |
42 | 63 | 1764 | 3969 | 2646 |
37 | 79 | 1369 | 6241 | 2923 |
47 | 86 | 2209 | 7396 | 4041 |
25 | 51 | 625 | 2601 | 1276 |
44 | 78 | 1936 | 6084 | 3432 |
41 | 83 | 1681 | 6889 | 3403 |
48 | 90 | 2304 | 8100 | 4320 |
35 | 65 | 1225 | 4225 | 2275 |
28 | 47 | 748 | 2209 | 1316 |
Covariance can be calculated as follows:
The values of two standard deviations can be calculated as follows:
Covariance: Covariance is a measure that is used to measure the relationship between the movements of two variables.
(b)
Determine the coefficient of correlation.
(b)
Explanation of Solution
The coefficient of correlation can be calculated by dividing the covariance with the product of the two sample deviations as follows:
Thus, the coefficient of correlation is calculated to be 0.8811.
(c)
Determine the coefficient of determination.
(c)
Explanation of Solution
The coefficient of determination can be calculated by squaring the coefficient of correlation as follows:
Thus, the coefficient of determination is calculated to be 0.7763.
(d)
Determine the least squares line.
(d)
Explanation of Solution
The covariance is calculated to be 98.52 and the value of
The values of
Similarly,
The value of
The least square line will thus be
(e)
Determine the indication of the least square line.
(e)
Explanation of Solution
The results show that there is a very strong positive linear relationship that exists between the two variables taken to analysis. This means that there is a strong positive linear relationship between the time taken to study and the marks obtained. Each additional hour for the study leads to an increase in the marks, and it is on an average by 1.705.
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Chapter 4 Solutions
Statistics for Management and Economics (Book Only)
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