I'm trying to find out how stocks and cash react (in terms of returns) when people feel bearish/bullish and when they move asset allocation between stocks/cash.
I have three data sets: monthly Dow jones closing prices, allocation of assets between cash and stocks, and monthly proportion(%) of bullish/bearish people. Would this be a linear regression as follows:
[Dji prices]$y_1$ + [cash]$y_1$ = $\alpha$ + [bearish %]$\beta_1$ + [bullish %]$\beta_2$ + [% allocation cash]$\beta_3$ + [% allocation stocks]$\beta_4$ + $e$
I am thinking to use the t-test and the null hypothesis being that $\beta_t$ = 0 where t=1, 2, 3, and 4. Does this mean I have to do 4 separate tests to test the significance of the four variables?
Is this the right approach to do a test to find the significance of each explanatory set?