Insignificant coefficent, hi R2

[davidnordstrom]

I estimated the following linear regression in Eviews:
Dependent Variable: PRIS
Method: Least Squares
Date: 07/12/10 Time: 16:35
Sample: 1 32
Included observations: 32

Variable Coefficient Std. Error t-Statistic Prob.

C 11.09973 64.36392 0.172453 0.8647
MARK 0.218873 0.404334 0.541318 0.5940
HHI 0.005354 0.006092 0.878820 0.3894
BEF 2.53E-07 2.74E-07 0.925223 0.3654
ABP 43.28024 35.65912 1.213721 0.2383
INK -0.000836 0.000508 -1.643722 0.1151
BIND 0.013654 0.187019 0.073011 0.9425
FOR -10.46322 15.48003 -0.675917 0.5065
TAL -9.853428 33.38539 -0.295142 0.7708
SMS -21.99989 15.40633 -1.427977 0.1680
INT -12.75087 13.08787 -0.974251 0.3410

R-squared 0.533996 Mean dependent var 50.80964
Adjusted R-squared 0.312090 S.D. dependent var 34.94941
S.E. of regression 28.98716 Akaike info criterion 9.837870
F-statistic 2.406401 Durbin-Watson stat 1.994475
Prob(F-statistic) 0.043242

All coefficents are insignificant on 10% level however R2 is still fairly high. P-value on F-stat is also significant. How do I interpret this? If no coefficents are significant then this should be a bad estimation of the dependent variable and I shouldn't receive such high values of r2 and F-stat. Isn't that a correct reasoning?

[startz]

Basically, you're seeing the results of multicollinearity. Taken together your equation does a reasonable job of explaining the dependent variable, but there isn't enough information to sort out which variables really matter.

[davidnordstrom]

when testing for multicollinearity i used confidence ellipse which implies that c(1) (intercept) and another coefficent is collinear. If i remove the other coefficent c(1) is now significant and R2 is slightly higher. I do not see the logic behind collinearity between the intercept and another coefficent though? If c(1) is estimated from the other data how can it be collinear with another coefficent?
Also when doing checked VIF analysis i recive values close to one on all parameters which would imply no multicollinearity, right?

[startz]

Removing a variable can only lower the R2. Something else has changed, perhaps the sample.

[davidnordstrom]

thanks for your quick answers! your right, it had actually decreased. still though how can i interpret c(1) and another coefficent to be collinear? and that c(1) becomes significant first after removing this coefficent?

[davidnordstrom]

I would really appreciate some assistance to the question how the intercept term and anotehr coefficent could be collinear

[startz]

The simplest example, which may not apply exactly in your case, is a set of dummies. Suppose D1=1 if x>0 and D1=0 otherwise. Suppose D2=1 if x<=0 and D2=0 otherwise. Then the constant term is perfectly collinear with D1 and D2.

[davidnordstrom]

i see your point. however it doesnt really apply in my case. im testing mobilprices for some number of variables. in my regression i get collinearity between a markets concentration ratio (measured as hhi) and the intercept. it doesnt apply to any economic reasoning so could it be just a coincidence that this happens?

[startz]

Loosely speaking, the intercept adjusts for the difference between the mean of the dependent variable and the means of the independent variables weighted by the coefficients. When you drop a variable, that changes the needed adjustment. In most cases, the intercept doesn't have a very interesting economic interpretation in any event.

[davidnordstrom]

thank you for the answers. this will help a lot for my thesis :)