7. Suppose that log(Y )i = B1 + B2 log(X)i + Ui ; where Y = the number of crimes

Question

7. Suppose that

log(Y )i = B1 + B2 log(X)i + Ui ;
where
Y = the number of crimes committed in the town
X = the number of police officers working in the town :
You, the researcher, wish to interpret this regression as a causal model of the
effect of X on Y .
(a) How would you interpret B2?
(b) How would your answer to part (a) change if the model had been defined with instead of log(X)?
(c) How would your answer to part (a) change if the model had been defined with Y instead of log(Y)?
(d) How would your answer to part (a) change if the model had been defined with Y instead of log(Y) and 1/X instead of log(X)?

Explanation / Answer

1) we will interpret B2 as linear multiplier 2) It will be declared a logrithmic multilpier along x axis 3) It will be declared a logrithmic multilpier along y axis 4) then It will be logrithmic reciprocal to one another

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