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… (24 more words) …

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… (98 more words) …

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… (16 more words) …

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