Discuss the pros and cons of raw regression estimates and st

Discuss the pros and cons of raw regression estimates and standardized regression estimates and discuss when each is appropriate.

Solution

Advantages of standarized regression estimates

Standard coefficients\' advocates note that the coefficients ignore the independent variable\'s scale of units, which makes comparisons easy.

Disadvantages

Critics voice concerns that such a standardization can be misleading. Since standardizing a variable removes the unit of measurement from its value, a standardized coefficient for a given relationship only represents its strength relative to the variation in the distributions. This invites bias due to sampling error when one standardizes variables using means and standard deviations based on small samples. Furthermore, a change of one standard deviation in one variable is only equivalent to a change of one standard deviation in another predictor insofar as the shapes of the two variables\' distributions resemble one another. The meaning of a standard deviation may vary markedly between non-normal distributions (e.g., when skewed or otherwise asymmetrical). This underscores the importance of normality assumptions in parametric statistics, and poses an additional problem when interpreting standardized coefficient estimates that even nonparametric regression does not solve when dealing with non-normal distributions.
Unstandardized relationships say that for a one-raw-unit increment on a predictor, the outcome variable increases (or if B is negative, decreases) by a number of its raw units corresponding to what the B coefficient is.

Standardized relationships say that for a one-standard deviation increment on a predictor, the outcome variable increasess (or decreases) by some number of SD\'s corresponding to what the coefficient is.

If the raw units are generally familiar (e.g., years, dollars, inches, miles, pounds), I\'d go with the unstandardized solution. However, if the variables\' raw units are not well-known in everyday usage (e.g., on a marital-satisfaction inventory with a maximum score of 50, what does one point really convey?), then I\'d use the standardized solution.