409exr_04_ans

# 409exr_04_ans - 4 [email protected] 2

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Econ 409 B. B±own S²±ing 2012 EXERCISE 4: A±sw²rs Taking y i = GPA i and x i = ACT i , we have the folowing calculations ( b ± 1 given below): iy i x i y i ± yx i ± x ( x i ± x ) 2 ( y i ± y )( x i ± x ) 1 2.8 21 -0.413 -4.875 23.77 2.01 2 3.4 24 0.188 -1.875 3.52 -0.35 3 3.0 -0.213 0.125 0.02 -0.03 4 3.5 27 0.288 1.125 1.27 0.32 5 3.³ 29 0.388 3.125 9.77 1.21 ³ 3.0 25 -0.213 -0.875 0.77 0.19 7 2.7 25 -0.513 -0.875 0.77 0.45 8 3.7 30 0.488 4.125 17.02 2.01 Total 25.7 207 0 0 5³.875 5.8125 ´ean 3.2125 25.875 1. Using the sixth and seventh columns above we have b ± 1 = P 8 i =1 ( y i ± y )( x i ± x ) P 8 i =1 ( x i ± x ) 2 = 5 : 8125 56 : 875 =0 ² 102 and b ± 0 = y ± b ± 1 x ² 5681 . The inte±ce²t sugest a ²ositive ±elationshi² betwen ACT sco±es and ultimate GPA with inc±eases in ACT sco±es ±esulting in co±±es²onding inc±eases in GPA of about one tenth as la±ge. The inte±ce²t sugests that ACT sco±es of ze±o wil ±esult, on ave±age, in GPA's of about .5³. This late± numbe± should not be taken se±iously, since the estimate is insigniµcantly dife±ent f±om ze±o and such an ACT sco±e is unlikely in any event, but instead taken as a way to make the slo²e ±es²onse mo±e acu±ate. If the ACT sco±e

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409exr_04_ans - 4 [email protected] 2

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