I have the following problem:
My Solution:
I'm trying to solve this problem by doing the following:
so we know that: $$ R^2 = \frac{SSE/(T-K)}{SST/(T-1)}$$
By plotting all the know values we get: $$ 0.952 = \frac{0.069/(25-5)}{SST/(25-1)}$$
$$ SST = \frac{(0.069/(25-5))(25-1)}{0.952}$$ so we get $$ SST = 0.91302$$
With SST know I would use this formula:
$$R^2 = 1 - \frac{SSE}{SST}$$
(By plotting all the values in brackets one by one instead of SSE, if one of the numbers has a high $R^2$ then we are dealing with a multicollinearity problem).
Question:
Could anyone possibly tell me if this is the right approach? (based off the number of points allocated to this question and the length of this method I have the feeling that it isn't correct)
Many thanks for your help!
Hard to tell something for sure without further information. Multicoliniearity is technically unstable inverse matrix $(X'X)^{-1}$, and as the variances of the coefficients are the main diagonal of $\sigma^2 (X'X)^{-1}$, then high standard deviations may indicate a presence of high multicoliniarity. On the other hand, you have only $25$ obsrvations, $5$ predictors (plus in the intercept term and the variance of $\epsilon$). That is, you are trying to estimate seven (!) parameters with only $25$ observations. Thus as the variance is inversely related to $n$, then the high standard deviations maybe also result of the pretty small sample size.