I'm trying to figure out whether how the S&P500 reacts from the change in bullish sentiments of people and the change in people's allocation in stocks. The bullish proportion and stock allocation are my explanatory variables (in percentage) and monthly S&P500 closing price is my independent variable. Below is an example snapshot of my data:
Date SP500 Stocks Bullish
1 2016-07-30 100 51 25
2 2016-08-30 109 40 32
3 2016-09-30 107 42 29
If I detrended my S&P500 monthly prices using the loess() function in R and got the cyclical components, how would I interpret the coefficients in regression model? If the coefficient for Stocks was 3, would it be that for every 1% increase in stocks allocation, that S&P500 prices would increase by 3 points? Because the prices are detrended, I think that I am interpreting the units of the regression output incorrectly, especially for the independent variable.