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I have the following problem:

question

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!

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

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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.

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