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Regression and Principal Component Analysis of Annual Flood and Yield Data, Exercises of Mathematical Statistics

Instructions for completing assignments related to statistical analysis of mean annual flood data and annual yield data. The tasks include obtaining regression equations, principal components, and cross correlations using given data sets.

Typology: Exercises

2012/2013

Uploaded on 04/20/2013

sathyanna
sathyanna 🇮🇳

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Assignment Module 7
1. Consider the observations of mean annual flood (Q in cumec) obtained in 15 different
watershed, as given in the table below. The mean annual flood is assumed to be
dependent on area of watershed (A in hectares), rainfall (P in cm) and basin length (L in
km). Obtain regression equation for Q in terms of remaining variables and obtain R2
value.
Q
P
A
L
89
107
92
35
140 108 369 55
408
104
349
56
371
106
527
93
301
107
357
54
242
105
167
47
682
107
1190
112
133 103 104 39
97
104
57
25
640
75
1012
91
335
76
410
46
85
79
165
41
436
76
1992
143
446 79 3401 265
83
91
79
24
2. Obtain the principal components for the data given in problem no.1
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Assignment – Module 7

  1. Consider the observations of mean annual flood (Q in cumec) obtained in 15 different watershed, as given in the table below. The mean annual flood is assumed to be dependent on area of watershed (A in hectares), rainfall (P in cm) and basin length (L in km). Obtain regression equation for Q in terms of remaining variables and obtain R^2 value. Q P A L 89 107 92 35 140 108 369 55 408 104 349 56 371 106 527 93 301 107 357 54 242 105 167 47 682 107 1190 112 133 103 104 39 97 104 57 25 640 75 1012 91 335 76 410 46 85 79 165 41 436 76 1992 143 446 79 3401 265 83 91 79 24
  2. Obtain the principal components for the data given in problem no.
  1. The annual yield of a basin (Y in mm) is to be obtained from annual rainfall (in mm) of 4 stations (A, B, C and D) in and around the basin is given below. Obtain the multiple regression equation using PCA. Y A B C D 929 556 1193 1569 834 1052 646 1048 2226 950 1120 568 1243 2111 810 1116 571 944 2016 982 1076 596 1208 1874 853 887 490 775 1690 969 876 395 673 1443 845 840 420 858 1128 768 861 385 698 1222 684 1129 457 1196 1687 1033 906 405 1037 1469 937 1082 475 1337 1823 1821 955 558 1300 1621 1753 1042 564 1095 1719 1612 1107 598 1194 1922 1919 1315 899 1750 2327 2583 999 420 843 1185 1420 925 483 1060 1199 1417 1146 678 1381 1914 1874
  2. Obtain the lag one cross correlation of annual rainfall data at two sites C and B in problem no. 3