A) \[\frac{b}{1-a}\]
B) \[\frac{1-a}{b}\]
C) \[\frac{\beta }{1-\beta }\]
D) \[\frac{a}{1-\alpha }\]
Correct Answer: A
Solution :
Let mean of \[x\]and \[y\]series are \[\bar{x}\]and\[\bar{y}.\] Lines of regression pass through mean \[(\bar{x},\bar{y}).\] \[\therefore \] \[\bar{y}=a\bar{x}+b,\bar{x}=\alpha \bar{y}+\beta \] Given that, \[\bar{x}=\bar{y}\] \[\therefore \] \[\bar{x}=a\bar{x}+b,\bar{x}=\alpha \bar{x}+\beta \] \[\Rightarrow \] \[\bar{x}=\frac{b}{1-a},\bar{x}=\frac{\beta }{1-\alpha }\]
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