John Spurrier
Department of Statistics
University of South Carolina
Comparing Two Regression Lines Over a Fixed Interval
Exact one-sided and two-sided simultaneous hyperbolic confidence bounds are
developed for the difference of two simple linear regression lines over a
finite interval for the predictor variable. It is assumed that the errors
are i.i.d. normal. The dual problem of testing equality of two regression
lines is also considered. No restrictions are made on the values of the
predictor variable in the training samples. After making a suitable
transformation, it is shown that the probability points used in these bounds
is a function of the size of an angle. These probability points are the
root of an equation involving a one-dimesional integral and are evaluated
numerically. It is shown that these probability points come from the same
distributions used by Wynn and Bloomfield (1971) and Bohrer and Francis
(1972) to bound a single simple linear regression over a finite interval.
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