Clarification pag. 189

[OrlandiMartina]

On page 189 ("Statistical Science") the text states that, if the identifiability condition is not satisfied, the slope coefficient would be equal to infinity.
Could you please clarify this point? In this situation the OLS estimator for the slope is given by the covariance between
x and y divided by the variance of x. If the identifiability condition fails, the denominator becomes zero. So should the slope be interpreted as not identifiable in that case? I would be grateful if you could explain what I am missing.

[Asadunipr]

@OrlandiMartina Thank you for your question.

Please see the attached note for the explanation.

indetifiability.pdf

[OrlandiMartina]

Thank you, Professor @Asadunipr , for the clarification. Now I understand that the reference to an “infinite slope” should only be interpreted as a geometric intuition.