Question

Consider the model Yi = 2 + βxi +E i , i = 1, 2, ....

Consider the model Yi = 2 + βxi +E i , i = 1, 2, . . . , n where E1, . . . , E n be a sequence of i.i.d. observations from N(0, σ2 ). and x1, . . . , xn are given constants.

(i) Find MLE for β and call it β. ˆ .

(ii) For a sample of size n = 7 let (x1, . . . , x7) = (0, 0, 1, 2, 3, 5, 6) and (y1, . . . , y7) = (2, 4, 5, 8, 8, 10, 13). Calculate βˆ.

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