LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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M.Sc. DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – APRIL 2008
ST 1812 – STATISTICAL COMPUTING – I
Date : 06/05/2008 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
Answer the following questions. Each question carries 33 marks
- (a) Write the quadratic form associated with the matrix
A =
Verify whether it is positive definite.
(b) Obtain the characteristic roots and vectors of the following matrix:
A =
Obtain the matrix U such that UTAU = L.
(OR)
Find the inverse of the following matrix by partitioning method or
sweep out process.
A =
Sale Price (in lakh Rs) | No. of Rooms | Age of building |
25.9 | 7 | 42 |
27.9 | 6 | 40 |
44 | 6 | 44 |
28.9 | 7 | 32 |
31.5 | 5 | 30 |
30.9 | 6 | 32 |
36.9 | 8 | 50 |
40.5 | 5 | 17 |
37.5 | 5 | 40 |
44.5 | 7 | 45 |
- The data on sale prices of houses are given below with information on the number of rooms and age of the building:
Build a model with an intercept. Test for overall significance and the significance of the individual regressors. Comment on the adequacy of the model.
(OR)
(a) A model with a maximum of four regressors is to be built using a sample of
size 30. Carry out ‘Stepwise Building Process’ to decide the significant
regressors given the following information:
SST = 1810.50, SSRes(X1) = 843.79, SSRes(X2) = 604.22, SSRes(X3) = 1292.93, SSRes(X4) = 589.24, SSRes(X1, X2) = 38.60, SSRes(X1, X3) = 818.05, SSRes(X1, X4) = 49.84, SSRes(X2,X3) = 276.96, SSRes(X2, X4) = 579.25, SSRes(X3,X4) = 117.16, SSRes(X1, X2, X3) = 32.07, SSRes(X1, X2, X4) = 31.98, SSRes(X1,X3, X4) =33.89, SSRes(X2, X3, X4) =49.21, SSRes(X1, X2, X3,X4) = 31.91
(b) The following are observed and predicted values of the dependent variable for a model with an intercept and two regressors.
Y | Y^ |
16.68 | 21.7 |
12.03 | 12.07 |
13.75 | 12.19 |
8 | 7.55 |
17.83 | 16.67 |
21.5 | 21.6 |
21 | 18.84 |
19.75 | 21.6 |
29 | 29.67 |
19 | 16.65 |
Compute the standardized residuals and find if there are any outliers.
- The number of accidents taking place in a high way is believed to have mixture
of two Poisson distributions with mixing proportion 2/7 and 5/7. Fit the
distribution for the following data corresponding to one such distribution.
Marks | Number of days |
0 | 98 |
1 | 78 |
2 | 56 |
3 | 73 |
4 | 40 |
5 | 8 |
6 | 2 |
7 | 1 |
>8 | 0 |
(OR)
- Generate Five observations from a Normal distribution with mean 20 and variance 36 truncated at zero
- Generate a sample of size 2 from a mixture of two Cauchy variates one of them has scale parameter 1 and location Parameter 1 and the other has Cauchy distribution with scale parameter 1 and location parameter 0.
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