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I had the possibility to try some regression on Football data.

I receive the following ouput: lm output

I receive a quite good R² but I wonder if it´s important that the intercept has no significance and a rather high std. error.

I also get the following qqPlot and I assume, my linear model is acceptable.

QQPlot

Maybe someone could help me to Interpret this result and clarify my doubts about the intercept.

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  • $\begingroup$ It might help to know a bit more about your data, what is the response variable and what are the covariates? $\endgroup$
    – M. Berk
    Jan 15 '14 at 15:30
  • $\begingroup$ Well, it is true that I had to admit that the data was standardized. So these are standardized coefficients. Y is the market value of a player and the other covariates are attributes like passing, shots on target etc. $\endgroup$ Jan 15 '14 at 15:36
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The intercept and its lack of significance is not a problem. The significance is testing if the intercept is zero (Ho: $b_0$=0) which isn't a test you are likely to be very interested in. If you scaled and centered your data, the intercept should be very close to zero. I would recommend removing the intercept from the model since you are working with standardized data.

The picture below represents the effect of centering data which came from a somewhat similar question (link here). See that the intercept is forced to be zero:

enter image description here

And as stated in another similar question (see the answer by Joshua here):

Removing the intercept is a different model, but there are plenty of examples where it is legitimate.[...]The case of standardized data. In some cases, one may be working with standardized data. In this case, the intercept is 0 by design.

Finally, the qqplot does look appropriate. (however take a look at point 63)

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  • $\begingroup$ thx but isnt it noteworthy that the residual Standard error is rather high? I assume that this modell is not able to predict my data well because of the Standard error. I receive quite bad results $\endgroup$ Jan 15 '14 at 16:01
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    $\begingroup$ Room for disagreement on the qqplot. There is one moderate outlier labelled 63. It would do no harm to review whether 30, 32, 63 are special in any sense. $\endgroup$
    – Nick Cox
    Jan 15 '14 at 16:07
  • $\begingroup$ Assuming that you are interested in this sport, you should be able to apply your qualitative knowledge. Is it really true that the response (whatever it is) is highly predictable in principle making high $R^2$ achievable? I don't follow any sport closely, but surprise after surprise about outcomes is what fuels some large fraction of sports journalism (setting aside tittle-tattle about the players). $\endgroup$
    – Nick Cox
    Jan 15 '14 at 16:11
  • $\begingroup$ I actually didn't see point 63 (not sure how). As Nick Cox suggested, perhaps you should take a look at it. $\endgroup$
    – Underminer
    Jan 15 '14 at 16:17
  • $\begingroup$ I couldn't really say if the RSE is high or not because it depends on the problem. Perhaps the response in naturally highly variable. Low RSE can be achieved by overfitting, but may not lead to good prediction. From another question: "The residual standard error is an estimate of the parameter σ.[...] The σ relates to the constant variance assumption; each residual has the same variance and that variance is equal to σ2." stats.stackexchange.com/questions/5135/… $\endgroup$
    – Underminer
    Jan 15 '14 at 16:18

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