Given are five observations for two variables, x and y.
xi 1 2 3 4 5
yi 3 8 6 12 14
S.No | X | Y | (x-x̅)2 | (y-y̅)2 | (x-x̅)(y-y̅) |
1 | 1 | 3 | 4.0000 | 31.3600 | 11.2000 |
2 | 2 | 8 | 1.0000 | 0.3600 | 0.6000 |
3 | 3 | 6 | 0.0000 | 6.7600 | 0.0000 |
4 | 4 | 12 | 1.0000 | 11.5600 | 3.4000 |
5 | 5 | 14 | 4.0000 | 29.1600 | 10.8000 |
Total | 15 | 43 | 10.0000 | 79.2000 | 26.0000 |
Mean | 3.000 | 8.600 | SSX | SSY | SXY |
SSE =Syy-(Sxy)2/Sxx= | 11.600 |
a)
error Variance σ2 = | s2 =SSE/(n-2) | = | 3.867 |
b)
std error σ = | se =√s2 | = | 1.966 |
c)
estimated standard error of slope =se(β1) = | s/√Sxx= | 0.622 |
d)
test stat t = | β1/se(β1)= | = | 4.18 |
p value: | = | 0.0249 |
e)
Source | DF | SS | MS | F |
regression | 1 | 67.6 | 67.600 | 17.48 |
Residual error | 3 | 11.6 | 3.867 | |
Total | 4 | 79.2 |
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 6 12 14
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