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Confidence intervals for factors+continuous variables

  1. Nov 26, 2008 #1
    I have

    [tex] y_{ij} = \mu_{i} + \alpha x_{ij} + e_{ij} [/tex]

    where [tex] i = 1, 2,3 [/tex] and [tex] j = 1, \ldots , r [/tex].
    [tex] \mu_{i} [/tex] represents the mean of the data set plus factor levels i , [tex] \alpha x_{ij} [/tex] is a continuous variable.

    So, the problem is the following:

    Construct confidence intervals for [tex] \mu_1 [/tex] , [tex] \mu_2 - \mu_1 [/tex] , and [tex] (\mu_3 - \mu_2) - (\mu_2 - \mu_1) [/tex].

    The original problem consisted of finding conf.intervals for the same things except the continuous variable wasn't in the model.
    I have looked around alot, but I can't find any instructions on confidence intervals when both factors and continuous variables are included.

    Help appreciated!
  2. jcsd
  3. Dec 8, 2008 #2
    You can think of it as follows:

    Without the x, y = m + e implies m = mean(y).

    When you have an x and the equation becomes y = m + ax + e, m = mean(y - ax), where a is the estimated slope coefficient.

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