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I am having a bit of trouble with square root transformation on a simple linear equation. I was given the following equation: Y = β1X + ε, where ε ~ N(0, σ2X). I need to show that with the square root transformation, it becomes a linear model with approximately constant variance. When I perform the square root transformation, I obtain the following equation √Y= √β1X + ε. I am having trouble knowing what to do with the information about the error.

kjetil b halvorsen
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compscinewb
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    Regardless of which variable you contemplate transforming, the claimed result is not always true. Among the problems are the possibility that $Y$ is negative--something you haven't ruled out. We will need to assume $\beta_1\gt 0$ and $X\gt 0.$ In that case you should be able to analyze this model as described at https://stats.stackexchange.com/a/35717/919, https://stats.stackexchange.com/a/496998/919, and https://stats.stackexchange.com/a/66038/919 (which I believe directly addresses your question). – whuber Dec 03 '21 at 18:40

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