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08_30ans - = =& n x x = 6 5 35 = =& n y y = 7 1&...

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2. A chemist wishes to study the relation between the drying time of a paint and the concentration of a base solvent that facilitates a smooth application. The data of concentration setting x and the observed drying times y are recorded in the table below. Plot the data and calculate the correlation coefficient. Concentration x Drying Time y 0 4 4 7 6 6 8 10 12 8 Consider the model Y i = β 0 + β 1 x i + ε i , where ε i ’s are i.i.d. N ( 0, σ 2 ) . Calculate 0 ° ˆ , 1 ° ˆ , ± ˆ , e s , and R 2 . x y x x - y y - ( ) 2 x x - ( ) 2 y y - ( ) ( ) y y x x - - 0 4 6 3 36 9 18 4 7 2 0 4 0 0 6 6 0 1 0 1 0 8 10 2 3 4 9 6 12 8 6 1 36 1 6 Total: 30 35 0 0 80 20 30 5 30 = = ° n x x = 6 5 35 = = °

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Unformatted text preview: = = & n x x = 6 5 35 = = & n y y = 7 1 & ˆ = ( ) ( ) ( ) 8 3 80 30 2 = = & &---x x y y x x = 0.375 . & ˆ = x y 1 & ˆ-= 7 – ( 0.375 ) ⋅ 6 = 4.75 . The least-squares regression line: y ˆ = 4.75 + 0.375 ⋅ x . x y y ˆ y y e ˆ-= 2 e 0 4 4.75 -0.75 0.5625 4 7 6.25 0.75 0.5625 6 6 7 -1 1.0000 8 10 7.75 2.25 5.0625 12 8 9.25 -1.25 1.5625 Total 0 8.75 ( ) & &-= 2 2 ˆ i i i y y e = 8.75 . ( ) &-= 2 2 ˆ 1 & ˆ i i y y n = 5 75 . 8 = 1.75 . 75 . 1 & ˆ = ≈ 1.3229 . ( ) &--= 2 2 ˆ 2 1 i i e y y n s = 3 75 . 8 ≈ 2.916667 . 916667 . 2 = e s ≈ 1.7078 . 20 75 . 8 2 1-= R = 0.5625 . 56.25%...
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