Why use confidence intervals with linear regression?
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There is a population regression line that exists out there... but we can only calculate a sample regression line.
y-hat is our estimate of what the actual mean response (µy) is at given predictor values.
b0 is our estimate (with our sample) of the actual y-intercept for the population.
b1 is our estimate (with our sample) of the actual change in predicted mean response for each unit +/- in our predictor variable.
µy is the population's mean response to given predictor variable values.
β0 is the actual y-intercept for the population's regression.
β1 is the actual change in the population's mean response for each unit +/- in our predictor variable.
With confidence intervals, we can do our best to set an interval that we believe the true population parameters (β0, β1, βk) lie within at a certain level of confidence!