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If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρρsatisfies.
- a)ρ = 0
- b)ρ > 0
- c)ρ = 1 or −1
- d)ρ < 0
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the two lines of regression of a bivariate distribution coincide, t...
If the two lines of regression of a bivariate distribution coincide, it means that there is a perfect linear relationship between the two variables. This can happen in two cases:
The two variables are perfectly positively correlated, meaning that as one variable increases, the other variable also increases by a fixed amount. In this case, the correlation coefficient will be equal to 1.
The two variables are perfectly negatively correlated, meaning that as one variable increases, the other variable decreases by a fixed amount. In this case, the correlation coefficient will be equal to -1.
Therefore, if the two lines of regression of a bivariate distribution coincide, the correlation coefficient will be equal to 1 or -1.
The correct answer is therefore (c) ρ = 1 or −1.
Most Upvoted Answer
If the two lines of regression of a bivariate distribution coincide, t...
If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient is +1 or -1, indicating a perfect linear relationship between the two variables.
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If the two lines of regression of a bivariate distribution coincide, then the correlation coefficientρρsatisfies.a)ρ = 0b)ρ > 0c)ρ = 1 or −1d)ρ < 0Correct answer is option 'C'. Can you explain this answer?
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