Does bootstrapped regression allow for inference?
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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
edited 2 days ago
Richard Hardy
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
$endgroup$
add a comment |
$begingroup$
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
edited 2 days ago
Richard Hardy
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
$endgroup$
add a comment |
$begingroup$
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
edited 2 days ago
Richard Hardy
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
$endgroup$
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
edited 2 days ago
Richard Hardy
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
edited 2 days ago
Richard Hardy
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
edited 2 days ago
Richard Hardy
28.2k642129
edited 2 days ago
Richard Hardy
28.2k642129
edited 2 days ago
Richard Hardy
28.2k642129
28.2k642129
asked Apr 8 at 21:15
VastingVasting
305
asked Apr 8 at 21:15
VastingVasting
305
asked Apr 8 at 21:15
VastingVasting
305
305
add a comment |
add a comment |
1 Answer
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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 $beta>0$.
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
$endgroup$
add a comment |
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1 Answer
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1 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 $beta>0$.
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
$endgroup$
add a comment |
$begingroup$
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 $beta>0$.
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
$endgroup$
add a comment |
$begingroup$
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 $beta>0$.
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
$endgroup$
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 $beta>0$.
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
edited Apr 8 at 21:31
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
answered Apr 8 at 21:25
Tim♦Tim
60k9133229
60k9133229
add a comment |
add a comment |
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