# 36 - The slope b and intercept a of the leastsquares line...

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The slope  b  and  intercept  a of the least-squares line are statistics. That is, we  calculated them from the  sample  data. Conditions for regression inference: We have n observations on an explanatory variable x and a response variable y.  Our goal is to study or predict the behavior of y for given values of x. For any fixed value of x, the response y varies according to a Normal  distribution.  Repeated responses y are independent of each other. The mean response μy has a straight-line relationship with x given by a  population regression line   μy =   +  x α β The slope   and intercept   are unknown parameters. β α The standard deviation of y (call it  ) is the same for all values of x. The σ   value of   is unknown. σ There are thus three population parameters that we must estimate from  the data:  ,  , and  .

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## This note was uploaded on 02/27/2012 for the course STAT 121 taught by Professor Patticolling during the Winter '11 term at BYU.

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36 - The slope b and intercept a of the leastsquares line...

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