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

Essay Question▾

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 Equation and the correlation coefficient is r.

Equation

Equation

Equation

Equation

Equation

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

… (32 more words) …

Question number: 2

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2013

Essay Question▾

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

Equation

Equation

Equation

Equation

the parital correlation between

… (104 more words) …

Question number: 3

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2012

Essay Question▾

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

… (144 more words) …

Question number: 4

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Given the following correlation matrix of order 3 x 3

Equation

Calculate (i) r 12.3 (ii) r 1.23

Explanation

In general, the correlation matrix is in these notations

Equation

(i)

Equation

Equation

Equation

Equation

(ii)

Equation

Equation

Equation

Question number: 5

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2009

Essay Question▾

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

Equation

Equation

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

Equation

Equation

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

Equation

Equation

The correlation coefficient is defined by

… (41 more words) …

Question number: 6

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2015

Essay Question▾

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

Equation

Equation

The relationship between the partial and multiple correlations is

Equation

Equation

Equation

Equation

Equation

Equation

Question number: 7

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

Appeared in Year: 2012

Essay Question▾

Describe in Detail

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

Equation

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

Explanation

First, we calculate the sample correlation coefficient r

Equation

for i = 1 to 10

Equation

Putting the value in the formula for n = 10

Equation

Equation

Equation

The test hypothesis is

Equation

The test statistic is the t-test

Equation

Equation

Equation

The tabulated value is t 0.05, 8

… (30 more words) …

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