Question on Impact of Independent Variable Interpretation

#1
Hi,

Suppose i have a normal linear regression construct, like
Sales = Intercept + M1*X1 + M2*X2 + M3*X3

Suppose X1,X2,X3 are the statistically significant variables from the model. I want to create some sort of a simulator which says , for X% increase in X1, what is increase in Y, likewise for X% increase in X2, what is increase in Y, and so on...

I know that typically, what we do is keep X2,X3 at average and multiply M1*X1 (Let's say this X1 value is 10 in first case, and then X1 value is 11 in 2nd case,..so here we have between the 2 scenarios we have increased X1 by 10% and hence i can measure what happens to Y keeping all other variables constant/median/average?)

PLease let me know if this is the right way to interpret this and if i am framing the question correctly?

Thanks!
 

hlsmith

Omega Contributor
#2
We are to assume all variables are continuous in formatting?


You can log all independent and the dependent variable, then all interpretation are approximately on the % scale. Look up log-log linear regression or elasticity. If doing this, you would want to double check your linear regression assumptions to make sure you did not introduce any issues.
 
#3
Most independent variables are % variables with values between 0-100% and 1 variable is a continuous variable with values of 0.2 to 1.5. Dependent variable is also a continuous variable with values from 0 to 1..,,

Basically, all my independent variables are % variables, except 1... Dependent variable is also a continous variable with values from 0 to 1...

Like in a normal regression, for the % Independent variable, can i not say "1 Unit/1 % increase in Independent variable results in (Beta/m1) increase in Dependent variable with all other variables being constant?. Please let me know.. I Want to quantify this..
 

hlsmith

Omega Contributor
#4
Are most of these percentage variable have centrally located mean without too much dispersion? If values hang out around the bounds there can be some issues and if dependent variable is % not centrally located beta regression may be a better fit. How do the model residuals look?