# 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

### Describe in Detail

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

Obtain correlation coefficient between X and Y

### Explanation

First find the marginal distribution of X

find the marginal distribution of Y

The mean of X and Y is

The second moment of X and Y is

The variance of X and Y

## Question number: 9

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2011

### 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

## Question number: 10

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2010

### 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.

where ρ=0.8, σ _{Y} =3.5, σ _{X} =2.5

The estimated regression equation of Y corresponding to X is

where

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