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Solve 15 questions on decision theory

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We received a test prep question bank to prepare for our final exam. I need solutions. This is not an assignment. This is a practice test questions.

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The solution gives detailed steps on solving 15 questions on decision theory. Lots of topics are covered.

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1.
Period Sales Moving average Absolute Error Squared Error
1 338
2 219
3 278 278.33 0.33 0.11
4 265 254 11 121
5 314 285.67 28.33 802.78
6 323 300.67 22.33 498.78

2.
Period Sales Moving average Absolute Error Squared Error
1 338
2 219 338
3 278 314.20 36.20 1310.44
4 265 306.96 41.96 1760.64
5 314 298.57 15.43 238.15
6 323 301.65 21.35 455.63

3.
For moving average, MSE=(0.11+121+802.78+498.78)/4=355.67 and for exponential smoothing, MSE=(1310.44+1760.64+238.15+455.63)/4=941.22. Since I prefer smaller MSE, moving average is the better method.

4.
Period Sales (Y) L B F
1 250 250 15
2 265 265 15 265
3 278 279.6 15 280
4 265 288.68 14.41 294.60
5 314 305.27 14.63 303.09
6 323 320.52 14.69 319.90

5.
Yes, trend component is significant because its p-value is 0 which is very small.

Yes, there is a seasonal trend if alpha is 0.10 because all p-values of quarters ...

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