Statistics 845.3 –Assignment 4

IA fertilizer manufacturer was interested in determining the "optimal" amount per acre of a new fertilizer (AA) that should be applied to produce maximum yield. To determine this quantity of fertilizer, the amount was varied from 0.0 units per acre to 4.0 units per acre in n = 21 test plots. The data is given the table below:

Table: the following table gives Y, yield per acre, when the amount of

fertilizer AA is applied at the rate of X units per acre.

i / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11
X / 0.0 / 0.2 / 0.4 / 0.6 / 0.8 / 1.0 / 1.2 / 1.4 / 1.6 / 1.8 / 2.0
Y / 13.73 / 10.3 / 14.98 / 18.2 / 18.64 / 19.27 / 18.53 / 19.66 / 22.15 / 24.27 / 27.12
i / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21
X / 2.2 / 2.4 / 2.6 / 2.8 / 3.0 / 3.2 / 3.4 / 3.6 / 3.8 / 4.0
Y / 24.78 / 28.14 / 21.72 / 18.97 / 20.24 / 19.17 / 13.96 / 12.49 / 6.51 / 4.07

a)Fit a polynomial regression model of degree 3 (cubic) to this data.

Y = 0 + 1X +2X2+ 3X3 + 

b)Carry out the sequence of tests:

  1. H0: 3 = 0 against HA: 3  0
  2. If H0 is accepted in i. test H0: 2 = 0, 3 = 0 against HA: 2  0 or 3  0.
  3. If H0 is accepted in ii. test H0: 1 = 0, 2 = 0, 3 = 0 against HA: i  0 for some i.

c)Estimate the value of X that would maximize the expected Yield per acre Y?

IIThe following data was collected from Canadian financial markets over a period of n= 60 months. One is interested in predicting the Monthly Return on Canadian Treasury Bills (Y) using the following independent variables

  1. (X1) The value of the Bank of Canada Assets.
  2. (X2) The Canadian Consumer Price Index.
  3. (X3) Canada/USA Spot Exchange Rate.
  4. (X4) Canada/USA One Month Forward Exchange Rate

The data on the next two pages:

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Month
i / (X1)
Bank of Canada Assets. / (X2)
Canadian Consumer Price Index / (X3) Canada/USA Spot Exchange Rate / (X4)
Canada/USA One Month Forward Exchange Rate / (Y)
Monthly Return on Canadian Treasury Bills
1 / 10400 / 61.2 / 1.01 / 1.01 / 8.59
2 / 10317 / 61.5 / 0.99 / 1 / 8.7
3 / 10580 / 61.7 / 0.98 / 0.99 / 9.04
4 / 10559 / 62 / 0.98 / 0.98 / 8.97
5 / 10504 / 62.5 / 0.98 / 0.98 / 8.94
6 / 10946 / 62.8 / 0.97 / 0.98 / 8.99
7 / 10995 / 63 / 0.96 / 0.97 / 9.02
8 / 10806 / 63.3 / 0.97 / 0.98 / 9.12
9 / 10830 / 63.6 / 0.97 / 0.97 / 8.97
10 / 11002 / 64 / 0.97 / 0.97 / 9.07
11 / 11759 / 64.2 / 0.97 / 0.97 / 8.88
12 / 11843 / 64.5 / 1.03 / 1.03 / 8.41
13 / 11362 / 65 / 1 / 1.01 / 8.08
14 / 11176 / 65.6 / 1.02 / 1.02 / 7.67
15 / 11687 / 66.3 / 1.04 / 1.05 / 7.61
16 / 12049 / 66.7 / 1.05 / 1.05 / 7.55
17 / 11830 / 67.2 / 1.04 / 1.04 / 7.26
18 / 12132 / 67.7 / 1.05 / 1.05 / 7.07
19 / 12348 / 68.3 / 1.05 / 1.05 / 7.12
20 / 12024 / 68.6 / 1.07 / 1.07 / 7.16
21 / 12107 / 69 / 1.07 / 1.07 / 7.09
22 / 12503 / 69.6 / 1.07 / 1.07 / 7.19
23 / 12303 / 70.1 / 1.1 / 1.1 / 7.25
24 / 13416 / 70.6 / 1.1 / 1.1 / 7.18
25 / 12471 / 70.8 / 1.09 / 1.09 / 7.14
26 / 12948 / 71.3 / 1.1 / 1.1 / 7.24
27 / 13439 / 72.1 / 1.11 / 1.11 / 7.62
28 / 13783 / 72.3 / 1.13 / 1.13 / 8.18
29 / 13119 / 73.3 / 1.12 / 1.12 / 8.13
30 / 13804 / 73.9 / 1.11 / 1.11 / 8.24
31 / 13541 / 75 / 1.12 / 1.12 / 8.43
32 / 13380 / 75.1 / 1.13 / 1.13 / 8.77
33 / 14464 / 74.9 / 1.15 / 1.15 / 9.02
34 / 16200 / 75.7 / 1.18 / 1.18 / 9.52
35 / 13889 / 76.3 / 1.16 / 1.16 / 10.29
36 / 15106 / 76.5 / 1.16 / 1.16 / 10.43
37 / 14012 / 77.1 / 1.18 / 1.18 / 10.8

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Month
i / (X1)
Bank of Canada Assets. / (X2)
Canadian Consumer Price Index / (X3) Canada/USA Spot Exchange Rate / (X4)
Canada/USA One Month Forward Exchange Rate / (Y)
Monthly Return on Canadian Treasury Bills
38 / 14291 / 77.8 / 1.2 / 1.2 / 10.78
39 / 14992 / 78.8 / 1.18 / 1.18 / 10.9
40 / 14841 / 79.3 / 1.15 / 1.15 / 10.84
41 / 14513 / 80.1 / 1.14 / 1.14 / 10.84
42 / 15338 / 80.5 / 1.16 / 1.16 / 10.82
43 / 14989 / 81.1 / 1.16 / 1.16 / 10.91
44 / 15636 / 81.4 / 1.17 / 1.17 / 11.32
45 / 16381 / 82.1 / 1.16 / 1.16 / 11.57
46 / 15133 / 82.7 / 1.16 / 1.15 / 12.86
47 / 15566 / 83.5 / 1.18 / 1.18 / 13.61
48 / 15746 / 84 / 1.16 / 1.16 / 13.63
49 / 14821 / 84.5 / 1.16 / 1.16 / 13.54
50 / 15010 / 85.2 / 1.15 / 1.15 / 13.56
51 / 17245 / 86.1 / 1.14 / 1.14 / 14.35
52 / 15705 / 86.6 / 1.19 / 1.19 / 15.64
53 / 16516 / 87.6 / 1.18 / 1.19 / 12.54
54 / 15956 / 88.6 / 1.15 / 1.16 / 11.15
55 / 16035 / 89.3 / 1.14 / 1.15 / 10.1
56 / 17476 / 90.1 / 1.15 / 1.15 / 10.21
57 / 16091 / 90.9 / 1.15 / 1.15 / 10.63
58 / 17044 / 91.7 / 1.17 / 1.16 / 11.57
59 / 17791 / 92.9 / 1.17 / 1.17 / 12.87
60 / 17313 / 93.4 / 1.19 / 1.18 / 16.31

Analyze this data to determine which factors determine the Monthly Return on Canadian Treasury Bills (Y).

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