# Statistical Methods-Correlation Coefficient (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 7 of 10

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## Question number: 1

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2009

### Describe in Detail

(i) Show that the arithmetic mean of (positive) regression coefficients is greater than the correlation coefficient.

(ii) What is the value of the product of geometric mean of variances and the geometric mean of regression coefficients?

### Explanation

(i) The arithmetic mean of regression coefficients is and the correlation coefficient is r.

The square of the two real numbers cannot be negative. So, the arithmetic mean of (positive) regression coefficients is greater than the correlation coefficient.

(ii) Geometric mean of variances is

## Question number: 2

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2013

### Describe in Detail

For a trivariate population, it is given that:

σ _{1} =3, σ _{2} =4, σ _{3} =5, r _{12} =0.7, r _{13} =0.6, r _{23} =0.4

Compute all partial and multiple correlation coefficients.

### Explanation

Given that there are three variable X _{1}, X _{2}, X _{3} for a trivariate population. The partial correlation coefficient is between any two variable eliminating the third variable. So, the parital correlation between X _{1} and X _{2} is

the parital correlation between

## Question number: 3

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2012

### Describe in Detail

Define partial correlation coefficient r _{12.3 } between x _{1} and x _{2} eliminating from each the effect of x _{3}. Derive the expression for r _{12.3 } and comment on its usefulness in multivariate data analysis.

### Explanation

Partial correlation coefficient defined as a association between any two variables out of a set of eliminating the other variable. Consider three variables X _{1}, X _{2} and X _{3}. Now we want to find out the partial correlation coefficient r _{12.3 } between X _{1} and X _{2}

## Question number: 4

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

### Describe in Detail

Given the following correlation matrix of order 3 x 3

Calculate (i) r _{12.3} (ii) r _{1.23}

### Explanation

In general, the correlation matrix is in these notations

(i)

(ii)

## Question number: 5

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2009

### Describe in Detail

The two regression lines between X and Y are 8X - 10Y + 66 = 0, 40X - 18Y = 214. The variance of X is 9. Find X, Y, σ _{Y} and ρ.

### Explanation

Given that

We know that the mean value of the given series satisfies the regression line that is

The means of X and Y is calculate by multiply equation (1) by 5 to subtract equation (2), we get

The correlation coefficient is defined by

## Question number: 6

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2015

### Describe in Detail

With 3 variables X _{1}, X _{2} and X _{3}, it is given that r _{13} =0.71, R _{1.23} =0.78. Find r _{12.3}.

### Explanation

We know that

The relationship between the partial and multiple correlations is

## Question number: 7

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

Appeared in Year: 2012

### Describe in Detail

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

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

### Explanation

First, we calculate the sample correlation coefficient r

for i = 1 to 10

Putting the value in the formula for n = 10

The test hypothesis is

The test statistic is the t-test

The tabulated value is t _{0.05, 8}