I have some questions about the interaction plot. I tried to make it on my own but I am wrong in my approach and I would like to know how to construct this. I have made a log linear regression with weekly data and I am interested in interactions between explanatory variables. My model is at follows :
$$ log(y_t) = log(\beta_0) + \beta_{1}log(x_{1,t}) + \beta_{2}log(x_{2,t}) + \beta_{3}x_{3,t} + ... + \beta_{n}x_{n,t} + \epsilon_{t} $$
So to construct my interaction plot in order to see interaction between the variable $x_1$ and the variable $x_2$, I define the function of $x_{1}$
$$ f_{x_{2,t} = a}(x_{1,t}) = log(\beta_0) + (\hat\beta_{1})log(x_{1,t}) + (\hat\beta_{2})log(a) + ... + (\hat\beta_{n})x_{n,t} + \epsilon_{t} $$
where I decided to fix the values for $x_{i,t}$, $i\neq 1$ and consider the variable for which I want to look the interaction with $x_1$ as a parameter fixed at $a$ and $\hat(\beta)$ are the parameter estimation. Then, I decided to consider the same function with another value parameter for $x_{2,t}$ that is
$$ f_{x_{2,t} = c}(x_{1,t}) = log(\beta_0) + (\hat\beta_{1})log(x_{1,t}) + (\hat\beta_{2})log(c) + ... + (\hat\beta_{n})x_{n,t} + \epsilon_{t} $$
But my approach seems not good because what is changing in my functions is just the ordinate at the origin, so I cannot use the criterion about parallel curves.. Is someone knows how my approach fails ? And also, is this kind of approach possible for continuous variable or are we limited to factor variables ?
Thank you a lot !
