Loyola College M.Sc. Statistics April 2008 Statistical Computing – I Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 35

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

  1. (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
  1. 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.

 

  1. 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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