# Coefficients and standard deviations

#### bobesp

##### New Member
Hi,

I have seen in a paper that the author states that the coefficient he gets in a regression implies that an increase of one standard deviation in the explanatory variable increases the dependent variable in 0.6%
How does the coefficient imply that? How did the author calculate that?

The thing is that now I am trying to write a report and want to make a similar statement, but I do not know how to calculate the change in the dependent variable when the explanatory variable changes in one standard deviation. I tried adding one stdev to all observations, but holding everything else constant, the coefficient did not change. What do I do? I'll really appreciate any help I can get here.

#### vinux

##### Dark Knight
Is it Multiple regression or Single Regression?
Are you going to connect standard deviation of Reg. Coefficient of an explanatory variable with dependent variable? ( or standard deviation of dependent variable ?)

#### astrodash

##### New Member
I does notmatter if it is linear or multiple regression, the interpretation od the coeficients is almost the same:

Linear regression: First of all, do not mention a change of 1 standard deviation since the coeficient of the independent variable is in terms of the variable units, and what it means is that "the coefficient value is the ratio on the change in the dependant variable when the independant variable changes its value in one unit" that is, i.e. if your model is y= a + bx and since a is the intercept value which is constant then y will change it value by b times when x increases or decreases its value by one unit. This is more evident by doing this: make a=0 and b=2 and if x=3 then y=6 but if x changes to 4 then y= 8 then by increasing x by one unit y changed its value according to the value of b variable, that is increased by 2 so it ended up in 8 (y + b)=(6 + 2) = 8.

Multiple regression:
The only difference here is that the changes in the dependant variable gets changed by the value of the coefficient of the changing independant variable while maintaining the other independant varaibles fixed, that is, it can change only one independant variable at a time to explain the value of the dependant variable.

Hope this helps. 