# How to check if a regression has a problem of multicollinearity?

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)

• The first formula for $R^2$ is not the right formula for it. The right formula is the second one, i.e. $1-\frac{SSE}{SST}$. Commented Jun 1, 2019 at 2:10

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.