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Assume that I cannot use least-squares estimator, so I don't have the intercept and the slope and only know one parameter at a time.

Is the intercept term in a simple linear regression a nuisance parameter when we want to test whether the slope is different from zero?

Is the slope term in a simple linear regression a nuisance parameter when we want to test whether the intercept is different from zero?

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  • $\begingroup$ The answer likely depends on what procedure or data you are using to "only know one parameter at a time." Please explain. $\endgroup$
    – whuber ♦
    Aug 5 at 13:56
  • $\begingroup$ Hi: $\hat{\beta}_1$ is independent of $\beta_{0}$ so I would think that not knowing the intercept should not matter when testing for the slope. On the other hand, the sums of squares terms of the model will change ( depending on whether you include the intercept ) and that part does effect the slope test so, as whuber said, you should probably explain your problem in more detail. $\endgroup$
    – mlofton
    Aug 5 at 14:15

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