Stat_425_Homework1.pdf - STAT 425 u2014 Fall 2020 Homework...

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STAT 425 — Fall 2020 Homework 1 (Posted on Wednesday September. 2; Due Thursday September. 17) Please submit your assignment following the Formatting Guidelines for Homework Submission. (Even if correct, answers might not receive credit if they are too difficult to read.) Remember to include relevant computer output. Unless otherwise stated, all data sets are from the faraway package in R . Unless otherwise stated, use a 5% level ( α = 0 . 05) in all tests. 1. The simple linear regression model is specified by y i = β 0 + β 1 x i + ε i , i = 1 , 2 , . . . , n with E( ε i ) = 0, var( ε i ) = σ 2 > 0, and cov( ε i , ε j ) = 0 if i 6 = j . The ordinary least squares estimates minimize the residual sum of squares RSS ( β 0 , β 1 ) = n X i =1 ( y i - β 0 - β 1 x i ) 2 (a) Take partial derivatives of RSS with respect to each parameter (separately), and set the resulting expressions equal to zero. (These are equivalent to what are called the normal equations .) (b) Solve the equations of the previous part simultaneously for β 0 and β 1 . Simplify your expressions to the form of the least squares estimates given in lecture.

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