In: Statistics and Probability
Advertising |
Sales |
||
(in $000s) |
(in $000s) |
||
1 |
30 |
184.4 |
|
2 |
40 |
279.1 |
|
3 |
40 |
244 |
|
4 |
50 |
314.2 |
|
5 |
60 |
382.2 |
|
6 |
70 |
450.2 |
|
7 |
70 |
423.6 |
|
8 |
70 |
410.2 |
|
9 |
80 |
500.4 |
|
10 |
90 |
505.3 |
|
sum |
600 |
3693.6 |
Calculate the sample covariance and also calculate the sample mean and variance for the advertising and sales variables.
These are the data that have been provided for the dependent and independent variable:
Obs. | X | Y |
1 | 30 | 184.4 |
2 | 40 | 279.1 |
3 | 40 | 244 |
4 | 50 | 314.2 |
5 | 60 | 382.2 |
6 | 70 | 450.2 |
7 | 70 | 423.6 |
8 | 70 | 410.2 |
9 | 80 | 500.4 |
10 | 90 | 505.3 |
We need to compute the covariance, which is computed by the first computing cross products of the sample data.
Now, with the provided sample data, we need to construct the following table, which will be used for the calculation of the covariance coefficient:
Therefore, based on the sample data provided, it is found that the sample covariance coefficient is
Advertising
Sales
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