# 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

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## 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 ρ. Then, we test the null hypothesis is that the relationship of random variable X and Y is not linear and the

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## 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

Rs. 72.6 are the most likely p

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