When doing a linear regression model, one calculates the coefficients called Beta and B, they are the values that display how much a dependent variable changes, depending on a predictor (or independent) variable.
What's the difference between standardized and unstandardized coefficients in linear regression models?
I guess you mean the following. Consider the simple linear regression model: $$Y_i = \beta_0 + \beta_1 X_i + \epsilon_i \qquad \epsilon_i \stackrel{d}{=} N(0,\sigma^2)$$.
One would estimate the $\beta_1$ with an Least-squares estimator $\hat \beta_1$, which expresses the expected amount $Y_i$ changes when $X_i$ increases by one.
This usually works (and is the easiest in terms of interpretation) but you could fit the model in some other ways
You could center the variable, for instance use $X_i^\ast = X_i - \overline X$ and fit the model once more, this would result in $$Y_i = \beta_0^\ast + \beta_1^*X_i^* + \epsilon_i^* \qquad \epsilon_i^\ast \stackrel{d}{=} N(0, \sigma^2)$$
then $\beta_1^\ast$ should be read as the expected increase in $Y_i$ when $X_i$ increases one from the mean. Using centered variables usually improves the model (it reduces multicollinearity). Also the value of $\beta_0^\ast$ is always usefull, it is the expected value of $Y_i$ hen $X_i = \overline X$.
You could standardizing the variables as wel, then $X_i^\ast = \dfrac{X_i-\overline X}{s_{X}}$, and refit the model.
The model then gives you the expected change in $Y_i$ when $X_i$ increases one standard deviation.
This has some numerical advantages.
Must usefull in multiple linear regression. Say you want a model like: $$Y_i = \beta_0 + \beta_1 X_{i1}+ \beta_2 X_{i2} + \epsilon_i \qquad \epsilon_i \stackrel{d}{=} N(0,\sigma^2)$$
How would you compare $\beta_1$ to $\beta_2$, in other words, which variable $X_1$ or $X_2$ has the most effect?
You could standardize the variables and the $Y$ values with $Y_i^\ast = \dfrac{Y_i - \overline Y}{s_Y}$ and the predictors as before. The $\beta_i^\ast$ which is the greatest (in absolute value) would point to the predictor which has the biggest effect.
