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I used Linear regression analysis with a sample and recieved the table below. How do I interpret the results?

The underlying problem is finding the greatest contributor to $SMTQ$.

  • $SMTQ$ - Sports Mental Toughness Questionaire
  • $Confa$ - Confidence
  • $Consa$ - Constancy
  • $Conta$ - Control

How do I understand the result sin the table? Is there any reason to calculate the standardized regression coefficients rather than the unstandardised ones listed in table? Should I present both values for a valid interpretation?

R output

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    $\begingroup$ Why do you think hierarchical is preferable, or even possible here? $\endgroup$
    – mdewey
    Commented Dec 23, 2021 at 15:11
  • $\begingroup$ We have an r2 value for total smtq rather than individual measures. When looking for the greatest predictor this would have been helpful. $\endgroup$
    – Grace
    Commented Dec 24, 2021 at 12:14
  • $\begingroup$ please indicate full form of your abrevitions and sime_thing about objectives of your study and the sample. $\endgroup$
    – user10619
    Commented Dec 26, 2021 at 7:52
  • $\begingroup$ Depending on what is the real question (we don't know it yet) I would use semipartial $R^2$ and use the bootstrap to get a 0.95 compatibility interval for the rank of predictor importance on this metric. For an example see Section 5.4 of RMS. Bootstrapping ranks fully exposes the difficulty of the ranking task and often will prevent one from declaring a clear winner. $\endgroup$ Commented Dec 27, 2021 at 13:06
  • $\begingroup$ See stats.meta.stackexchange.com/a/4554/919 for the close reasons. $\endgroup$
    – whuber
    Commented Jan 30, 2022 at 17:31

1 Answer 1

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You have only one statistically significant covariate, which is 'smtq$confa' with p-value 4.65e-13. Other coefficients are not statistically significant even at 10% level. Standardization would not affect the p-values. Hierarchical or multiple linear regression would not give you different results in your setup, given the magnitude of the p-values for different coefficients.

So, the covariate 'smtq$confa' is the best predictor in your problem.

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  • $\begingroup$ Thank you for your input. What values are best to present when discussing the findings? $\endgroup$
    – Grace
    Commented Dec 23, 2021 at 11:46
  • $\begingroup$ It depends on the field of your study. In Statistics related works, usually the detailed output of the computation, which you have presented in the question, is presented first. Then, the significant predictors are stated based on the p-values. Finally, the implications are discussed. In other fields, where the statistical methodology is used only to identify the significant variables, the implications are more stressed upon, and the variables which are not statistically significant are ignored from the discussion or presentation. $\endgroup$
    – joy
    Commented Dec 23, 2021 at 12:29
  • $\begingroup$ pvalues of such t-test for the covariates would not be affected by standardization. An an example, compare the pvalues obtained in this answer. $\endgroup$
    – joy
    Commented Dec 24, 2021 at 5:40
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    $\begingroup$ @joy statistical "significance" is an arbitrary concept that should not play a role here. $\endgroup$ Commented Dec 27, 2021 at 13:03
  • $\begingroup$ @FrankHarrell it is not clear to me why would you call statistical significance an arbitrary concept, although I agree that it depends on the nominal level, which is (somewhat arbitrarily) set to 5%, 1%, etc. In this particular case, from the p-values, it is seen that only one p-value is not only small but effectively 0, while others are relatively large. So, it will be 'statistically significant' according to its definition for almost any arbitrarily set nominal level. $\endgroup$
    – joy
    Commented Dec 27, 2021 at 13:20

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