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I am trying to determine if I can use the y-intercept of a simple linear regression to predict the slope but I want to confirm whether the y-intercept is spuriously correlated with the slope. Would this occur when the x values and y values can only be between a certain range? I found an earlier post that mentioned "in simple linear regression, the correlation between the estimated slope and intercept has the opposite sign of the mean of the explanatory variables. I.e., if the mean of the explanatory variables is positive, the correlation between the estimated coefficients will be negative and vice versa.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$ Commented Dec 2, 2024 at 21:11
  • $\begingroup$ Unless the explanatory data are centered at 0, there is always a non-zero correlation between the least squares estimates of intercept and slope, regardless of the ranges of the data. Could you perhaps explain what application you have in mind where you would have only the estimated intercept but not the estimated slope? $\endgroup$ Commented Dec 2, 2024 at 21:20
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    $\begingroup$ You will want to distinguish between (intercept, slope) qua parameter of the model, which you appear to consider random variables, and their estimates. Do you have data that permit you to do that, such as repeated experiments with collections of $(x,y)$ observations? $\endgroup$ Commented Dec 2, 2024 at 22:36
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    $\begingroup$ Somewhat related: Correlation between OLS estimators for intercept and slope. $\endgroup$ Commented Dec 2, 2024 at 22:40
  • $\begingroup$ @whuber I have repeated collections of observational data for many (300+) food web variables necessary to make TMS (d15N and contaminant concentration in each organism). I'm not sure if this data permits me to do that $\endgroup$ Commented Dec 3, 2024 at 13:30

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