ch8 supp sol

ch8 supp sol - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306 INTRODUCTORY STATISTICS Sem 1 2008/2009 1. X Hrs studied 15 28 13 20 4 10 Y Grade-point index 1.0 2.7 1.3 1.9 0.9 1.7 a) The line of best fit for these data using the formulas is: x y 0686 . 0 5543 . 0 ˆ + = (I) METHOD using the formulas is: XX XY S S x n x y x n xy b x b y a = = = = = 2 2 1 0 β = + + + = 1 . 166 7 . 1 10 ........ 7 . 2 28 1 15 x x x xy 1694 10 ......... 28 15 2 2 2 2 = + + + = x = 90 x = 5 . 9 y 6 = n 15 = x 5833333 . 1 = y
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0686 . 0 344 6 . 23 15 6 1694 ) 583333 . 1 15 6 ( 1 . 166 2 1 = = = = = XX XY S S x x x b β 5543 . 0 15 0686 . 0 583333 . 1 0 = = = = x x b y a x x bx a y 0686 . 0 5543 . 0 ˆ 1 0 + = + = + = (II) METHOD using the calculator only is: Press: MODE 2 SHIFT AC (LR appears on screen) 15 1 DATA, 28 2.7 DATA, D D y x , D D y x , ……………………………, 10 1.7 DATA D D y x , Check: Kout n gives n=6 SHIFT A gives 0 = a = 0.554263565 SHIFT B gives 1 = b = 0.068604651 SHIFT r gives ρ ˆ = r = 0.84859 ----- FOR Q1 f) (II)
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b) A plot of the data and the regression line: 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 5 10 15 20 25 30 To plot the least squares regression line we need to calculate 2 points. We can use the two answers calculated in c) (20, 1.926) and d) (0, 0.5543). c) Find y ˆ when x=20. The grade point index for a student who studies 20 hours per week is 926 . 1 20 0686 . 0 5543 . 0 ˆ = + = x y d) Find y ˆ when x=0. The grade point index for a student who studies 0 hours per week is 5543 . 0 0 0686 . 0 5543 . 0 ˆ = + = x y (the y-intercept) e) The prediction which is more reliable is c), because c) is INTERPOLATION whereas d) is EXTRAPOLATION. f) The correlation coefficient is 0.8485988
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(I) METHOD using the formula: 29 . 17 7 . 1 . .......... 7 . 2 1 2 2 2 2 = + + + = y 248333341 . 2 583333 . 1 6 29 . 17 2 2 2 = = = x y n y S YY 8485988 . 0
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ch8 supp sol - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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