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Is regression scale invariant?
Generally, regression with no regularisation (e.g. OLS) is scale invariant, and regularised regression (e.g. ridge regression) is not scale invariant, because the minimisers of the function change (ref).
What does invariance mean in statistics?
A system, function, or statistic has scale invariance if changing the scale by a certain amount does not change the system, function, or statistic’s shape or properties. Fractals are one of the more well known examples of this. For example, if you zoom in on a Koch snowflake, it looks the same.
Which is the interpretation of a logarithmic regression model?
3.4 Log-log model: logYi = + logXi + i In instances where both the dependent variable and independent variable(s) are log-transformed variables, the interpretation is a combination of the linear-log and log-linear cases above. In other words, the interpretation is given as an expected percentage change in Y when X increases by some percentage.
How is a regression coefficient related to log of Y?
Since this is just an ordinary least squares regression, we can easily interpret a regression coefficient, say β 1, as the expected change in log of y with respect to a one-unit increase in x 1 holding all other variables at any fixed value, assuming that x 1 enters the model only as a main effect.
How do I interpret a regression model when some…?
In summary, when the outcome variable is log transformed, it is natural to interpret the exponentiated regression coefficients. These values correspond to changes in the ratio of the expected geometric means of the original outcome variable. Some (not all) predictor variables are log transformed
How is OLS used in a regression model?
OLS regression of the original variable (y) is used to to estimate the expected arithmetic mean and OLS regression of the log transformed outcome variable is to estimated the expected geometric mean of the original variable. Now let’s move on to a model with a single binary predictor variable.