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The set of bivariate observation (x1, y1), (x2, y2),..... (xn, yn) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between x and y are
  • a)
    0 and 1 only
  • b)
    0 and –1 only
  • c)
    0, 1 and –1
  • d)
    –1 and 1 only
Correct answer is option 'D'. Can you explain this answer?
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The set of bivariate observation (x1, y1), (x2, y2),..... (xn, yn) are...
If set of bi-variate observation fall in a straight line with non-zero slope, then the values of correlation coefficient is -1 and 1 only.
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The set of bivariate observation (x1, y1), (x2, y2),..... (xn, yn) are...
1 only
c)-1 and 1 only
d)0 only

The correct answer is c) -1 and 1 only.

The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between two variables. It takes values between -1 and 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

In this case, all the observations fall on a straight line with non-zero slope. This means that there is a perfect linear relationship between x and y, either positive or negative. Therefore, the possible values of the correlation coefficient are -1 and 1 only.
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The set of bivariate observation (x1, y1), (x2, y2),..... (xn, yn) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then the possible values of the correlation coefficient between x and y area)0 and 1 onlyb)0 and –1 onlyc)0, 1 and –1d)–1 and 1 onlyCorrect answer is option 'D'. Can you explain this answer?
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