Hi Alycat,

Standardized variables have a mean of zero and unit variance (SD=1). This means that a unit increase in the standardized variable is equivalent to a standard deviation increase in the unscaled variable.

On average, with all other things being equal, a SD increase of X is associated with a (beta) increase in Y. If Y is also standardized, a SD increase in X is associated with a (beta)*SD increase in Y. Since the variables have been scaled, those covariates with larger standardized regression coefficients have a larger effect on the response variable.

Standardized regression coefficients can also be less interpretable in some respects: In your example, a standard deviation increase in the number of siblings may not really be meaningful if the SD is something like 0.5 or 1.2. I would recommend centering age (subtracting its mean), and standardizing TELD, leaving the number of siblings unscaled. This will give the intercept an actual interpretable meaning (average value of TOM for a child with 0 siblings, average TELD score, and average age), and have regression coefficients that scale naturally: an increase of one sibling, an increase in one year of age, a SD increase in test score.

Hope that helps.