Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.<br>Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.

Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:

A

1, 2 and 3

B

1, 3 and 4

C

Both 2 and 4

D

2, 3 and 4

Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$ and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:

A

1, 2 and 3

B

1, 3 and 4

C

3, 4 and 5

D

2, 3 and 5

The values in one of the series in a bivariate data set are multiplied by a constant K, which of the following would change as a result of this? A. Karl Pearson's coefficient of correlation B. Standard deviation C. Covariance between the variables D. Rank correlation coefficient Choose the correct answer from the options given below:

A

A, B and C only

B

B and C only

C

A, and D only

D

A, B, and D only

Which of the following statements is false? 1. When value of correlation coefficient is one, the two regression lines coincide 2. The regression coefficients are independent of the change of origin and of scale 3. The sign of the regression coefficients are always the same 4. The square of the coefficient of correlation is called coefficient of determination

A

1

B

2

C

3

D

4

Which of the following statements are true? a. The correlation coefficient is dependent on the choice of both origin and scale observations. b. The correlation coefficient is dependent on the units of measurements. c. The coefficient of correlation is the square root of the coefficient of determination. d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable.

A

a and b are true

B

a, b and c are true

C

c and d are true

D

Only d is true.

Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the coefficient of correlation.

A

Both (A) and (R) are true

B

(A) is true, but (R) is false

C

(A) is false, but (R) is true

D

Both (A) and (R) are false

Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the co-efficient of correlation.
On the basis of the above, choose the appropriate answer :

A

(A) and (R) are correct

B

(A) is correct, but (R) is not correct

C

(A) is not correct, but (R) is correct

D

Both (A) and (R) are not correct

Consider the following statements regarding inspection and quality control: 1. Coefficient of variation is a relative measure of dispersion. 2. Standard deviation is the root mean square of the deviation of all the results. 3. Standard deviation is relative measure of dispersion. 4. Lower value of standard deviation indicates low degree of uniformity of observations. Which of the above statements are correct?

A

1 and 4 only

B

2 and 3 only

C

1 and 2 only

D

2 and 4 only

Abeer has 14 novels. Abeer’s friend Sanjay takes 3 of them and gives 2 novels to Abeer. Abeer donates 7 novels but buys 4. Joy takes 4 novels from Abeer and gives him 5. Abeer takes one novel from Sanjay and gives it to Joy in exchange for 3 more. Abeer gives those 3 novels to Sanjay and he gives Abeer a novel and a magazine. Rahul takes the magazine which Sanjay gave to Abeer and gives Abeer a textbook. Abeer gives the textbook to Joy in exchange for a novel. Rahul takes the novel from Sanjay, gives it to Joy for a magazine and gives Abeer the magazine for a novel. How many textbooks does Abeer have?

A

0

B

1

C

2

D

3

Consider the following statements: 1) If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other. 2) If the correlation coefficient rxy = + 1, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

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