Statistical Methods-Correlation Coefficient (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 8 - 10 of 10

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Question number: 8

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2010

Essay Question▾

Describe in Detail

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

Equation

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

Equation

Equation

Equation

Equation

find the marginal distribution of Y

Equation

Equation

Equation

Equation

The mean of X and Y is

Equation

Equation

Equation

Equation

The second moment of X and Y is

Equation

Equation

Equation

Equation

The variance of X and Y

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Question number: 9

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

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Question number: 10

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2010

Essay Question▾

Describe in Detail

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.

Equation

where ρ=0.8, σ Y =3.5, σ X =2.5

Equation

The estimated regression equation of Y corresponding to X is

Equation

where Equation

Equation

Equation

Equation

Rs. 72.6

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