I am fitting two variables that seem to have a power relationship (y=a*x^b). If I log-transform both variables, they should have a linear relationship (ln(y) = c*ln(x) + d. Notice that b=c and ln(a)=d. However, when I fit the power and linear equation to these, respectively, the estimated coefficients do not satisfy these relationships. Expectedly, R-square is also different. I tried changing the fit options and didn't manage to make the two fittings equivalent. Has anyone any idea why this happens?
PS. fitting in excel is satisfying these relationships and I get identical values