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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:
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 
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.
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?
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.
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.
Determine the corrections or otherwise of the following Assertion and Reason : Assertion : For longitudinal static stability of an aircraft, slope of moment curve should be negative. Reason: Positive slope will result in more static stability than negative slope. Hence, slope should be positive always. and are true and is the correct reason for b) Both and are true but is not the correct reason for c) is true but is false d) is false but 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.
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 :
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:
Rajat beats Nitin by 240 m in a 1560 m race. Then they go to race on a slope where Rajat starts from bottom of the slope and Nitin starts from top of the slope they run towards each other and when they meet Nitin has travelled 20 m more than Rajat. If the speed of any person on the slope, compared to normal speed, becomes (150/11)%  more in decline and 10% less in incline, what was the total length of the slope?