Ls4202_endsem_2016 please answer only question no.6. (5 marks) 4. Write down the

Question

Ls4202_endsem_2016

please answer only question no.6. (5 marks)

4. Write down the expression for the Akaike Information Criterion (AIC) and explain its components? What is the basis of its use in mocdel selection? The proportion or males versus females anong green turtle Iatchliugs is a function of incubation temperature. A student conducted observations at two sites corresponding to low and high teamperature values and found that below 25 C (low temperature) the proportion of males PL was 0.6 and above 28°C (high temperature) the proportion of males Pu was 0.2. Derive a logistie regression model to predict the proportion of males among hatchlings of the green turtle as a fumetion of low aud high temperatures. How is the slope o, related to the ODDS ratio 6. Six thorphossetric meastremeuts Y,wewe talen on a mature flower for n individuals of a plant species. Show how you can use Principul Components Anelysis to order these n Section I1: Answer all questions. Marks: 2x 10-20 7. The following matrix has data on tlhe presruce or ahsenee of a ronlithom associatel witha recessive allele in two Imma populatious A ael B We are inteestel in testing if the incil-nre of the condition is different letmn the two Peniatsen what litt 11 vuur u 11 In just I,.7 ^^1.fere: fnun. -ttuby h..ni u dy, t- llls

Explanation / Answer

Let us suppose that the data on ‘n’ individuals on 6 species is of the following type.

Obs. No

Y1

Y2

Y3

Y4

Y5

Y6

1

Y11

Y12

Y13

Y14

Y15

Y16

2

Y21

Y22

Y23

Y24

Y25

Y26

3

Y31

Y32

Y33

Y34

Y35

Y36

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n

Yn1

Yn2

Yn3

Yn4

Yn5

Yn6

In order to perform Principal Component Analysis, assume that number of observations n > 6.

Now, when we perform PCA through any software usually we come with the following output.

PC1

PC2

PC3

PC4

PC5

PC6

Eigen Value

1

2

3

4

5

6

Proportion

Cumulative Proportion

In the above table proportion gives the ration of Eigen value to sum of all Eigen values. These values lies between 0 and 1. The cumulative proportion is the cumulative sum of proportion in second row and its last value is always 1.

Score table:

PC1

PC2

PC3

PC4

PC5

PC6

Y1

C11

C12

C131

C14

C15

C16

Y2

C21

C22

C23

C24

C25

C26

Y3

C31

C32

C331

C34

C35

C36

Y4

C41

C42

C43

C44

C45

C46

Y5

C51

C52

C53

C54

C55

C56

Y6

C61

C62

C63

C64

C65

C66

Using this PC scores let is develop another score variable as follows;

Z1 = C11*Y1 + C21*Y2 + C31*Y3 + C41*Y4 + C51*Y5 + C61*Y6

and

Z1 = C12*Y1 + C22*Y2 + C32*Y3 + C42*Y4 + C52*Y5 + C62*Y6

These two Z1 and Z2 will serve the purpose of representing ‘n’ observations on 6 variables in two dimensional space.

Obs. No

Y1

Y2

Y3

Y4

Y5

Y6

1

Y11

Y12

Y13

Y14

Y15

Y16

2

Y21

Y22

Y23

Y24

Y25

Y26

3

Y31

Y32

Y33

Y34

Y35

Y36

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n

Yn1

Yn2

Yn3

Yn4

Yn5

Yn6

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