HP 10BII Manual
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7: Statistical Calculations 91 Linear Estimation. 7KHVWUDLJKWOLQHFDOFXODWHGE\OLQHDUUHJUHVVLRQFDQ EHXVHGWRHVWLPDWHD \YDOXHIRUDJLYHQ [YDOXHRUYLFHYHUVD (QWHUWKH [\ GDWDXVLQJWKHLQVWUXFWLRQVRQSDJH (QWHUWKHNQRZQ [YDOXHRU \YDOXH n7RHVWLPDWH [IRUWKHJLYHQ \HQWHUWKH \YDOXHWKHQSUHVV*3 n7RHVWLPDWH \IRUWKHJLYHQ [HQWHUWKH [YDOXHWKHQSUHVV*4 Example: Forecasting. $OL·V$]DOHDVDGYHUWLVHVRQDORFDOUDGLRVWDWLRQ )RUWKHSDVWVL[ZHHNVWKHPDQDJHUKDVNHSWUHFRUGVRIWKHQXPEHURI PLQXWHVRIDGYHUWLVLQJWKDWZHUHSXUFKDVHGDQGWKHVDOHVIRUWKDWZHHN :KDWLVWKH \LQWHUFHSWWKHVORSHDQGWKHFRUUHODWLRQFRHIILFLHQW Week Minutes of Advertising (x-values) Sales (y-values) 12345678 1,000.00 2,000.00 3,000.00 y x b Sales in Dollarsm = 425.88 Minutes of Advertising (forecasted) 10B.book Page 91 Wednesday, June 21, 2000 5:19 PM
92 7: Statistical Calculations (VWLPDWHZKDWWKHOHYHORIVDOHVZRXOGEHLIWKHEXVLQHVVSXUFKDVHGRU PLQXWHVRIDGYHUWLVLQJ +RZPDQ\PLQXWHVRIDGYHUWLVLQJVKRXOG$OL·VEX\WRDWWDLQVDOHVRI Keys: Display: Description: *j0.00&OHDUVVWDWLVWLFDOUHJLVWHUV 0A1.00(QWHUVPLQXWHVDQGVDOHV IRUFRQVHFXWLYHZHHNV 0A2.00 0A3.00 0A4.00 0A5.00 0A6.00 *4376.25&DOFXODWHV\LQWHUFHSW E\f *i425.88LVSOD\VVORSH *3*i0.90&DOFXODWHVFRUUHODWLRQ FRHIILFLHQW *43,357.38(VWLPDWHVVDOHVLI PLQXWHVRIDGYHUWLVLQJ ZHUHSXUFKDVHG *43,783.25(VWLPDWHVVDOHVLI PLQXWHVZHUHSXU FKDVHG *36.16(VWLPDWHVPLQXWHVRI DGYHUWLVLQJUHTXLUHGIRU LQVDOHV 10B.book Page 92 Wednesday, June 21, 2000 5:19 PM
7: Statistical Calculations 93 Weighted Mean 7KHIROORZLQJSURFHGXUHFDOFXODWHVWKHZHLJKWHGPHDQRIGDWDSRLQWV[ [ « [QRFFXUULQJZLWKZHLJKWV \\« \Q 8VH 0DQGAWRHQWHU [\ SDLUV7KH \YDOXHVDUHWKHZHLJKWVRI WKH [YDOXHV 3UHVV *E Example. $VXUYH\RIRQHEHGURRPUHQWDODSDUWPHQWVUHYHDOVWKDW RIWKHPUHQWIRUSHUPRQWKIRUIRUDQGIRU :KDWLVWKHDYHUDJHPRQWKO\UHQW Keys: Display: Description: *j0.00&OHDUVVWDWLVWLFV PHPRU\ 0A1.00(QWHUVILUVWUHQWDQGLWV ZHLJKW 0A2.00(QWHUVVHFRQGUHQWDQG LWVZHLJKW 0A3.00(QWHUVWKLUGUHQWDQG LWVZHLJKW 0A4.00(QWHUVIRXUWKUHQWDQG LWVZHLJKW *E509.44&DOFXODWHVZHLJKWHG PHDQ 10B.book Page 93 Wednesday, June 21, 2000 5:19 PM
8: Additional Examples 95 8 Additional Examples Business Applications Setting a Sales Price 2QHPHWKRGIRUVHWWLQJWKHSHUXQLWVDOHVSULFHLVWRGHWHUPLQHWKHFRVWRI SURGXFWLRQSHUXQLWDQGWKHQPXOWLSO\E\WKHGHVLUHGUDWHRIUHWXUQ)RU WKLVPHWKRGWREHDFFXUDWH\RXPXVWLGHQWLI\DOOFRVWVDVVRFLDWHGZLWKWKH SURGXFW 7KHIROORZLQJHTXDWLRQFDOFXODWHVXQLWSULFHEDVHGRQWRWDOFRVWDQGUDWH RIUHWXUQ 35,&( 727$/&267¸ 180%(52)81,76ï \b571¸ \f\f Example. 7RSURGXFHXQLWV\RXUFRVWLV
96 8: Additional Examples Forecasting Based on History 2QHPHWKRGRIIRUHFDVWLQJVDOHVPDQXIDFWXULQJUDWHVRUH[SHQVHVLV UHYLHZLQJKLVWRULFDOWUHQGV2QFH\RXKDYHKLVWRULFDOGDWDWKHGDWDDUHILW WRDFXUYHWKDWKDVWLPHRQWKH[D[LVDQGTXDQWLW\RQWKH \D[LV Example. *LYHQWKHIROORZLQJVDOHVGDWDZKDWDUHWKHVDOHVHVWLPDWHVIRU \HDUVVL[DQGVHYHQ Year Sales $ 1 10,000 211,210 3 13,060 4 16,075 5 20,590 Keys: Display: Description: *j0.00&OHDUVVWDWLVWLFVUHJLVWHUV 0A1.00(QWHUVILUVW\HDUDQGVDOHV IRUWKDW\HDU 0A2.00(QWHUVVHFRQG\HDU·VGDWD 0A3.00&RQWLQXHVGDWDHQWU\ 0A4.00 0A5.00 *422,000.50(VWLPDWHVVDOHVIRU\HDU VL[ *424,605.00(VWLPDWHVVDOHVIRU\HDU VHYHQ 10B.book Page 96 Wednesday, June 21, 2000 5:19 PM
8: Additional Examples 97 Cost of Not Taking a Cash Discount $FDVKGLVFRXQWJLYHVDEX\HUDUHGXFWLRQLQSULFHLIWKHSD\PHQWLVPDGH ZLWKLQDVSHFLILHGWLPHSHULRG)RUH[DPSOH´1(7µPHDQVWKDW WKHEX\HUFDQGHGXFWSHUFHQWLISD\PHQWLVPDGHZLWKLQGD\V,I SD\PHQWLVQRWPDGHZLWKLQGD\VWKHIXOODPRXQWPXVWEHSDLGE\WKH WKGD\
98 8: Additional Examples Loans and Mortgages Simple Annual Interest Example.
100 8: Additional Examples Example. $QLQYHVWRUZLVKHVWRSXUFKDVHDPRUWJDJHWDNHQ RXWDW\bIRU\HDUV6LQFHWKHPRUWJDJHZDVLVVXHGPRQWKO\ SD\PHQWVKDYHEHHQPDGH7KHORDQLVWREHSDLGLQIXOODEDOORRQ SD\PHQW\fDWWKHHQGRILWVILIWK\HDU:KDWLVWKH\LHOGWRWKHSXUFKDVHULI WKHSULFHRIWKHPRUWJDJHLV Step 1. &DOFXODWH 3070DNHVXUH )9 6HWWR(QG0RGH3UHVV *OLIBEGINDQQXQFLDWRULVGLVSOD\HG Step 2. (QWHUWKHQHZYDOXHIRU 1LQGLFDWLQJZKHQWKHEDOORRQRFFXUV WKHQILQG )9WKHDPRXQWRIWKHEDOORRQ Keys: Display: Description: *b12.006HWVSD\PHQWVSHU\HDU .9.006WRUHVLQWHUHVWUDWH *U240.006WRUHVQXPEHURIPRQWKV (–100,000.006WRUHVRULJLQDODPRXQWRI PRUWJDJH /0.00(QWHUVDPRXQWOHIWWRSD\ DIWHU\HDUV 2899.73&DOFXODWHVUHJXODU SD\PHQW Keys: Display: Description: *L2899.735RXQGVSD\PHQWWR WZRGHFLPDOSODFHVIRU DFFXUDF\ *U60.006WRUHVQXPEHURI SD\PHQWVXQWLOEDOORRQ /88,706.74&DOFXODWHVEDOORRQ SD\PHQWDGGWRILQDO SD\PHQW\f 10B.book Page 100 Wednesday, June 21, 2000 5:19 PM