Statistical Methods-Correlation Coefficient (ISS Statistics Paper I (Old Subjective Pattern)): Questions 7 - 10 of 10

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Question number: 7

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

Appeared in Year: 2012

Essay Question▾

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For a set of 10 pairs of observations (x i, y j), i = 1 (1) 10, the following calculations are available

xi=61,xi2=412,yi=45,yi2=308,xiyi=295

Examine at 5 % level of significance if the two variables arc uncorrelated in the population.

Explanation

First, we calculate the sample correlation coefficient r

r=(xix)(yiy)(xix)2(yiy)2

for i = 1 to 10

r… (173 more words) …

Question number: 8

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2010

Essay Question▾

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Let (X, Y) be jointly distributed with density function

f(x,y)={x+y;0<x<1,0<y<10;otherwise

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

g(x)=01f(x,y)dy

=01(x+y)dy

=[xy+y22]01

=x+12… (374 more words) …

Question number: 9

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2011

Essay Question▾

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Describe a test of independence of two normal random variables based on r, the sample correlation coefficient using the t distribution. If n = 10 and r = 0.9, then carry out the test.

Explanation

Let X 1, X 2, …, X n and Y 1, Y 2, …, Y n are samples variables and the correlation coefficient of between this paired samples is denoted by r. If X’s and Y’s are follows independent normal random variables and correlation coefficient is… (164 more words) …

Question number: 10

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2010

Essay Question▾

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Find the most likely price in Mumbai corresponding to the price of Rs. 70 at Kolkata from the following:

Kolkata

Mumbai

Average price

65

67

Standard deviation

2.5

3.5

Correlation coefficient between the prices of commodities in the two cities is 0.8.

Explanation

First we find the regression coefficient β YX where Y is the price at Mumbai and X is the price at Kolkata.

βYX=ρσYσX

where ρ=0.8, σ Y =3.5, σ X =2.5

βYX=0.83.52.5=1.12

The estimated… (82 more words) …

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