Multiple Regression on time series variables with dummies

Question

I am trying to adjust seasonality on time series (8 years) independent variables (197 variables) by regressing these variables on monthly dummies. I have coded my dummies as follows:

dummy1 <- model.matrix( ~ intraMonth, data = AnovaDataAll)

Thereafter, I regress the Dependent Variable on each of the variable with the dummy variable:

MultReg <- lapply(CorData[c(-1, -c(195:293))], function(x) summary(lm(formula = ReturnIndex ~ x + dummy1, data = CorData))) 

The Regression Analysis gives me following results for (eg first variable = equity):

$equity

Call:
lm(formula = ReturnIndex ~ x + dummy1, data = CorData)

Residuals:
    Min      1Q  Median      3Q     Max 
-49.273  -5.263   0.640   5.560  45.373 

Coefficients: (1 not defined because of singularities)
                   Estimate Std. Error t value Pr(>|t|)  
(Intercept)         -0.7610     1.9749  -0.385   0.7002  
x                   -0.3586     0.6165  -0.582   0.5611  
dummy1(Intercept)        NA         NA      NA       NA  
dummy1intraMonth2    4.8220     2.8404   1.698   0.0903 .
dummy1intraMonth3    2.5903     2.7683   0.936   0.3500  
dummy1intraMonth4    1.7586     2.8082   0.626   0.5315  
dummy1intraMonth5    1.6997     2.7823   0.611   0.5416  
dummy1intraMonth6    3.1196     2.8143   1.108   0.2683  
dummy1intraMonth7    2.5446     2.7546   0.924   0.3562  
dummy1intraMonth8   -1.7986     2.7646  -0.651   0.5157  
dummy1intraMonth9    2.5249     2.7768   0.909   0.3637  
dummy1intraMonth10   1.9284     2.7982   0.689   0.4911  
dummy1intraMonth11   3.9216     2.7773   1.412   0.1587  
dummy1intraMonth12   0.9890     2.9464   0.336   0.7373  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 11.55 on 406 degrees of freedom
Multiple R-squared:  0.02259,   Adjusted R-squared:  -0.006298 
F-statistic: 0.782 on 12 and 406 DF,  p-value: 0.6692

I am wondering, if I have successfully conducted a seasonal adjustment on my Regression model. Moreover, I would like to rank all variables on statistical significance by looking at their t statistics. Based on the upper Output, do I simply have to look at the "x" row and take the t value of -0.582? How do I interpret the intercept of the first dummy (in this case January Dummy)? Does it matter, if I set the intercept on the December dummy rather on January?

Answer 1

Based on the upper Output, do I simply have to look at the "x" row and take the t value of -0.582?

Yes.

How do I interpret the intercept of the first dummy (in this case January Dummy)? Does it matter, if I set the intercept on the December dummy rather on January?

You only get 11 dummy variables(eg two categorise - one variable, so on). You can have any of the month as the intercept.