I am working on checking for constant variance in linear models and checking by looking at the plot of studentized residuals with fitted values. My data set via the plot looks to have a constant variance. I did a spread level plot on the data and it gives a suggested power transformation. 1.12, using this I fit a new model and checked the spread level plot again, which gives a power transformation of 1.05. I changed the power transformation to 1.05 and repeated this process many times. I finally settled on a power transformation of 1.252. After I refit the model to reflect the power transformation(1.252) and ran the spread level plot again. The suggested power transformation for this was 1.00068.
What I am wondering is If you can get the suggested power transformation to be very close to 1, does that mean the now has constant variance?