LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 29

FIRST SEMESTER – APRIL 2006

                                                 ST 1812 – STATISTICAL COMPUTING – I

 

 

Date & Time : 22-04-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

 

 

 

Answer any THREE questions

 

1. a) Find a G- inverse of the matrix

A =

 

1. b) Check whether the following vectors are linearly dependent:
2. i) X¢  = (1, -1, 2),       Y¢ = (2, 0, -1),             Z¢ = (0, -2, -5).
3. ii) X¢ = (1, 0,0), Y¢ = (0, 1, 0), Z¢ = (0, 0, 1).                            (20+14)

 

2. a) The following data relates to the results of an experiment the relative frequencies for 4 different types of genes are expected to be and
   where 0 < < 1.

The frequencies observed were 508, 432, 397 and 518 respectively.  Estimate

the parameter q by the method of maximum likelihood and find the estimate of

the  standard error of the estimator.

 

1. b) The scores of 17 students are given by the following table. Assuming that this

is a sample from normal population whose variance is s², obtain

1. a 95% confidence interval for s
2. a 99% confidence interval for s

 

Scores:

(Out of 100)         45     65     68     77     95     69     56         72        75

38     68     72     65     42     66     55         62

(14+20)

 

3. a) Below are given two random samples drawn from different normal populations:

Sample 1:    10        6          16        17     13     12     8       14     15        9

Sample 2:    7          13        22        15     12     14     18     8       21        23 10

 

Obtain a 99% confidences limits for the difference of means of the 2 populations.

 

1. b) Fit a normal distribution to the following data

 

C.I:	60-65	65-70	70-75	75-80	80-85	85-90	90-95	95-100
Frequency	3	21	150	335	325	135	26	4

(20+14)

 

4. a) Fit a multiple regression model of Y on X₁ and X₂ for the following data. Estimate Y when X₁ = 1350 sq.ft and X₂ = 2 years                                      (20)

 

1. b) Also, test the significance of the population multiple correlation coefficient at

5% level of significance.                                                                                (14)

 

FLAT PRIZE IN LAKHS (Y)	FLAT SIZE IN SQ.FT (X1)	AGE OF THE FLAT IN YEARS        (X2)
12.3	1050	1
15	1200	1
14.8	1180	3
11	950	2
10.3	900	3
16.9	1300	3
18	1400	3
6	450	4
5.2	480	5
4.6	420	4
18	1450	6
9.3	850	3
12.2	1020	7

 

5. a) Use Step-wise regression analysis to identify the most significant independent

variable(s) and comment on your finding regarding the significance of

population regression coefficients for the data given in question-4                (20)

1. b) Compute the condition index for the data in question-4 and examine whether

the multi-co linearity problem is present in the data or not.                          (14)

 

 

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