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Dr. Hackney STA Solutions pg 186

# Dr. Hackney STA Solutions pg 186 - 11-14 Solutions Manual...

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11-14 Solutions Manual for Statistical Inference 11.34 a. ANOVA table for height data Source df SS MS F Regression 1 60.36 60.36 50.7 Residual 6 7.14 1.19 Total 7 67.50 The least squares line is ˆ y = 35 . 18 + . 93 x . b. Since y i - ¯ y = ( y i - ˆ y i ) + (ˆ y i - ¯ y ), we just need to show that the cross term is zero. n i =1 ( y i - ˆ y i )(ˆ y i - ¯ y ) = n i =1 y i - α + ˆ βx i ) α + ˆ βx i ) - ¯ y = n i =1 y i - ¯ y ) - ˆ β ( x i - ¯ x ) ˆ β ( x i - ¯ x ) α = ¯ y - ˆ β ¯ x ) = ˆ β n i =1 ( x i - ¯ x )( y i - ¯ y ) - ˆ β 2 n i =1 ( x i - ¯ x ) 2 = 0 , from the definition of ˆ β . c. y i - ¯ y ) 2 = ˆ β 2 ( x i - ¯ x ) 2 = S 2 xy S xx . 11.35 a. For the least squares estimate: d i ( y i - θx 2 i ) 2 = 2 i ( y i - θx 2 i ) x 2 i = 0 which implies ˆ θ = i y i x 2 i i x 4 i . b. The log likelihood is
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