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Does bootstrapped regression allow for inference?

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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

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

asked Apr 8 at 21:15

VastingVasting

305

$endgroup$

add a comment | 

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

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

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

share|cite|improve this question

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

asked Apr 8 at 21:15

VastingVasting

305

$endgroup$

share|cite|improve this question

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

asked Apr 8 at 21:15

VastingVasting

305

share|cite|improve this question

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

asked Apr 8 at 21:15

VastingVasting

305

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

edited Apr 9 at 7:16

Richard Hardy

28.5k644131

asked Apr 8 at 21:15

VastingVasting

305

asked Apr 8 at 21:15

VastingVasting

305

1 Answer
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oldest

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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

edited Apr 8 at 21:31

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

$endgroup$

add a comment | 

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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

edited Apr 8 at 21:31

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

$endgroup$

add a comment | 

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

edited Apr 8 at 21:31

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

$endgroup$

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 $beta>0$.

share|cite|improve this answer

edited Apr 8 at 21:31

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

$endgroup$

share|cite|improve this answer

edited Apr 8 at 21:31

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230

answered Apr 8 at 21:25

Tim♦Tim

60.9k9135230