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Does bootstrapped regression allow for inference?



The 2019 Stack Overflow Developer Survey Results Are InObtaining and interpreting bootstrapped confidence intervals from hierarchical dataDistribution of reciprocal of regression coefficientHow to determine if predictor in piece-wise linear regression is significant?Non-technical conditions for validity of nonparametric bootstrap confidence intervalsBootstrapped coefficients for ordinal logistic regression with Rbootstrapped standard error to make inference about difference of meansBootstrapping multivariate multiple variable regressionFor a Fisher Information matrix $I(theta)$ of multiple variables, is it true that $I(theta) = nI_1(theta)$?Bootstrapping to measure the significance of the skewnessBootstrapped confidence interval for the difference in means for paired data



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$begingroup$


Assuming a linear model of
$$ y = beta_0+beta_1x+epsilon $$
I can construct a bootstrapped confidence interval for the estimate of $beta_1$ by sampling with replacement from all of the $(x_i, y_i)$ pairs from the data.



Is it possible for me to tell if the value of $beta_1$ is significant, without preforming a t-test the data? Or is the bootstrap used more less for inference but more for trying to find the most accurate predictor in this case?






statistical-significance inference bootstrap







share|cite|improve this question











$endgroup$


















    1












    $begingroup$


    Assuming a linear model of
    $$ y = beta_0+beta_1x+epsilon $$
    I can construct a bootstrapped confidence interval for the estimate of $beta_1$ by sampling with replacement from all of the $(x_i, y_i)$ pairs from the data.



    Is it possible for me to tell if the value of $beta_1$ is significant, without preforming a t-test the data? Or is the bootstrap used more less for inference but more for trying to find the most accurate predictor in this case?






    statistical-significance inference bootstrap







    share|cite|improve this question











    $endgroup$














      1












      1








      1





      $begingroup$


      Assuming a linear model of
      $$ y = beta_0+beta_1x+epsilon $$
      I can construct a bootstrapped confidence interval for the estimate of $beta_1$ by sampling with replacement from all of the $(x_i, y_i)$ pairs from the data.



      Is it possible for me to tell if the value of $beta_1$ is significant, without preforming a t-test the data? Or is the bootstrap used more less for inference but more for trying to find the most accurate predictor in this case?






      statistical-significance inference bootstrap







      share|cite|improve this question











      $endgroup$




      Assuming a linear model of
      $$ y = beta_0+beta_1x+epsilon $$
      I can construct a bootstrapped confidence interval for the estimate of $beta_1$ by sampling with replacement from all of the $(x_i, y_i)$ pairs from the data.



      Is it possible for me to tell if the value of $beta_1$ is significant, without preforming a t-test the data? Or is the bootstrap used more less for inference but more for trying to find the most accurate predictor in this case?






      statistical-significance inference bootstrap




      statistical-significance inference bootstrap






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited yesterday









      Richard Hardy

      28.2k642129




      28.2k642129










      asked 2 days ago









      VastingVasting

      305




      305




















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          4












          $begingroup$


          Is it possible for me to tell if the value of $beta_1$ is
          significant, without preforming a t-test the data?




          Yes. You could use bootstrap to calculate confidence intervals. Another thing that you could do, is you could take many bootstrap samples from your data, then calculate regression parameters for each of the samples and check how often the parameters calculated on bootstrap samples are greater then zero, where the empirical fraction from bootstrap samples would be equivalent of testing that $beta>0$.






          share|cite|improve this answer











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            $begingroup$


            Is it possible for me to tell if the value of $beta_1$ is
            significant, without preforming a t-test the data?




            Yes. You could use bootstrap to calculate confidence intervals. Another thing that you could do, is you could take many bootstrap samples from your data, then calculate regression parameters for each of the samples and check how often the parameters calculated on bootstrap samples are greater then zero, where the empirical fraction from bootstrap samples would be equivalent of testing that $beta>0$.






            share|cite|improve this answer











            $endgroup$

















              4












              $begingroup$


              Is it possible for me to tell if the value of $beta_1$ is
              significant, without preforming a t-test the data?




              Yes. You could use bootstrap to calculate confidence intervals. Another thing that you could do, is you could take many bootstrap samples from your data, then calculate regression parameters for each of the samples and check how often the parameters calculated on bootstrap samples are greater then zero, where the empirical fraction from bootstrap samples would be equivalent of testing that $beta>0$.






              share|cite|improve this answer











              $endgroup$















                4












                4








                4





                $begingroup$


                Is it possible for me to tell if the value of $beta_1$ is
                significant, without preforming a t-test the data?




                Yes. You could use bootstrap to calculate confidence intervals. Another thing that you could do, is you could take many bootstrap samples from your data, then calculate regression parameters for each of the samples and check how often the parameters calculated on bootstrap samples are greater then zero, where the empirical fraction from bootstrap samples would be equivalent of testing that $beta>0$.






                share|cite|improve this answer











                $endgroup$




                Is it possible for me to tell if the value of $beta_1$ is
                significant, without preforming a t-test the data?




                Yes. You could use bootstrap to calculate confidence intervals. Another thing that you could do, is you could take many bootstrap samples from your data, then calculate regression parameters for each of the samples and check how often the parameters calculated on bootstrap samples are greater then zero, where the empirical fraction from bootstrap samples would be equivalent of testing that $beta>0$.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 2 days ago

























                answered 2 days ago









                Tim♦Tim

                60k9133228




                60k9133228



























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