4. Calculate Population cov(x,y), Sample cov(x,y) from the following data
X | Y |
300 | 800 |
350 | 900 |
400 | 1000 |
450 | 1100 |
500 | 1200 |
550 | 1300 |
600 | 1400 |
650 | 1500 |
700 | 1600 |
Solution:
Mean `bar x = (sum x_i)/n`
`=(300+350+400+450+500+550+600+650+700)/9`
`=4500/9`
`=500`
Mean `bar y = (sum y_i)/n`
`=(800+900+1000+1100+1200+1300+1400+1500+1600)/9`
`=10800/9`
`=1200`
`x` | `y` | `X=(x-500)/50` | `Y=(y-1200)/100` | `X*Y` |
300 | 800 | -4 | -4 | 16 |
350 | 900 | -3 | -3 | 9 |
400 | 1000 | -2 | -2 | 4 |
450 | 1100 | -1 | -1 | 1 |
500 | 1200 | 0 | 0 | 0 |
550 | 1300 | 1 | 1 | 1 |
600 | 1400 | 2 | 2 | 4 |
650 | 1500 | 3 | 3 | 9 |
700 | 1600 | 4 | 4 | 16 |
--- | --- | --- | --- | --- |
`4500` | `10800` | `sum X=0` | `sum Y=0` | `sum X*Y=60` |
Population Cov(x,y) :
Population `Cov(x,y) = (sum (x-bar x)(y-bar y))/(n)`
`=60/9`
`=6.6667`
Sample Cov(x,y) :
Sample `Cov(x,y) = (sum (x-bar x)(y-bar y))/(n-1)`
`=60/8`
`=7.5`
This material is intended as a summary. Use your textbook for detail explanation.
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