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

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

Suppose that we have N independent variables (X1, X2, Xn) and dependent variable is Y. Now Imagine that you are applying linear regression by fitting the best fit line using least square error on this data. You found that correlation coefficient for one of its variable(Say X1) with Y is -0.95. Which of the following is true for X1?

A

relation between the x1 and y is weak

B

relation between the x1 and y is strong

C

relation between the x1 and y is neutral

D

correlation can't judge the relationship

Which of the following statements are correct?
1. Correlation analysis helps in determining the relationship between two or more variables. It does not tell us anything about the cause and effect relationship.
2. The ratio of explained variation to the total variation is called the coefficient of correlation.
3. Pearsonian coefficient always assumes linear relationship, and is unduly effected by the extreme items.

A

1 and 2

B

1 and 3

C

2 and 3

D

1, 2 and 3

The ratio of the covariance between x and y written as cov (x, y) to the product of the standard deviation of x and y symbolically

A

$$\frac{{\sum {\text{xy}}}}{{\sqrt {\sum {{\text{x}}^2} \cdot \sum {{\text{y}}^2}} }}$$

B

$${\text{r}} = \frac{{\operatorname{cov} \left( {{\text{x}},{\text{y}}} \right)}}{{\sigma {\text{x}},\,\sigma {\text{y}}}}$$

C

$$\frac{{\sqrt \sum {{\text{x}}^2}\sum {{\text{y}}^2}}}{{\sum {\text{xy}}}}$$

D

None of these

The . . . . . . . . error of correlation is an amount which if added to and subtracted from the average correlation coefficient produces amounts within which the chances are even that a coefficient of correlation from a series error selected at random will fall.

A

standard

B

probable

C

average

D

sample

The ratio of bed slope and the slope of energy line is 2, calculate the value of slope of energy line if the length of back water curve is 20000m. Given: E1=2m and E2=5m.

A

0.5×10-4

B

1.0×10-4

C

1.5×10-4

D

2.0×10-4

If dy/dx=3×10-4 m and the ratio of bed slope and slope of energy line is 0.7, calculate the value of slope of energy line if the uniform flow depth is 1.6m, critical depth is 1.2m.

A

5.25×10-4

B

6.25×10-4

C

7.2510-4

D

8.25×10-4