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I performed linear regression analysis to assess the associations between continuous variables. I found a significant p-value but my confidence interval includes zero. What does it mean? Here are the results;

β= -0.267

SE: 0.000

95 CI= -0.002 to 0.000

p=0.000

Results

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    $\begingroup$ This output seems to be unrelated to the question, because there is no interval shown that includes zero. The two intervals are $[0.7, 2.1]$ and $[-0.0017, -0.0004]$. $\endgroup$
    – whuber
    May 13 at 12:20

1 Answer 1

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Thank you for the screenshot. The unstandardized coefficient is $-0.00108$ (rounded to three significant digits) with a corresponding 95% confidence interval of $(-0.00172; -0.000445)$ and a $p$-value of $0.000996$. The $p$-value is below $0.05$ and correspondingly, the 95% confidence interval does not include $0$. There is no contradiction.

The standardized coefficient is $-0.267$ but a confidence interval is not provided for this coefficient. The $p$-value does not change, however. If you're interested in calculating a confidence interval for the standardized coefficient, I have summarized the steps in my answer to another post.

As @NickCox rightly states: The predictor is probably on a large scale which leads to very small coefficients and confidence limits because the coefficients are for an increase in 1 unit. To get the change per $x$ units, divide the predictor by $x$ before calculating the regression. For example: If the predictor is money in US dollars, divide by 1000 to calculate the change for an increase in \$1000.

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    $\begingroup$ This. Plus there is a presentation problem here. To avoid absurd numbers of decimal places, divide your predictor by some convenient number such as 1 thousand or 1 million. $\endgroup$
    – Nick Cox
    May 13 at 12:21

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