We are working on a multivariate linear regression model. Our objective is to forecast the quarterly % growth in mortgage loans outstanding.
The independent variables are: 1) Dow Jones level. 2) % change in Dow Jones over past quarter. 3) Case Shiller housing price index. 4) % change in Case Shiller housing price index over past quarter.
In a stepwise regression process, all above variables were selected. And, variables 1) and 3) were surprisingly significant. But, that is when used in combination. Somehow, there is something about the difference in those two indeces that does partly explain the % change in mortgage loans outstanding.
For my part, I find variables 1) and 3) problematic. This is because I believe they are heteroskedastic. And, their respective coefficients confidence interval are therefore unreliable. I also think they may have multicollinearity issues with their related variables based on % change. They may also cause some autocorrelation issues.
However, at first it seems some of my concerns may be overstated. After graphing the residuals of the whole model they seem OK. They don't trend upward. So, it appears the heteroskedasticity is not an issue for the whole model. Multicollinearity is not too bad. The variable with the highest VIF is around 5 much lower than the usual threshold of 10.
Nevertheless, I am still somewhat concerned that even though the whole model seems OK; the specific regression coefficients of the mentioned variables may not be (or more specifically the related confidence intervals).