Log-lin model in simple regression:
y_{i}=B_{0}.B_{1}^{Xi}.e^{ui} take natural log of both sides lny_{i}=lnB_{0} + (lnB_{1})x_{i} + u_{i} . Take lny_{i} = w_{i}, lnB_{0}= B^{*}_{0} and lnB_{1}=B^{*}_{1} so the former equation equals to w_{i}= B^{*}_{0} + B^{*}_{1} + u_{i}. It is said that, when you increase x by 1 unit, you expect B^{*}_{1} % change in y.
B^{*}_{1} =(dy_{i}/y_{i}) / dx_{i} = = (((y_{i}-y_{i-1})/y_{i}) / (x_{i}- x_{i-1}))*100 . question is about the numerator, (y_{i}-y_{i-1})/y_{i})*100:
1)It is said that the numerator reflects the percentage change in y, then why it is not ((y_{i}-y_{i-1})/y_{i-1}) but instead ((y_{i}-y_{i-1})/y_{i}) ? Why don't we divide by y_{i-1} (the value before i-th term,or the past value) instead of y_{i} (the i-th term, or the current value) ?
2) Does ((y_{i}-y_{i-1})/y_{i})*100 really stand for the percentage change in y?
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Log-lin model in simple regression: yi=B0.B1Xi.eui take natural log of both sides lnyi=lnB0 + (lnB1)xi +...
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