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A?5;>AB8 A;54C5B >ACI5AB2;OBL A CG5B>G25==>- :;8289 @538>=0 2>745;K20=8O, >@30=870F8>==>9 8 M:>=>9 F5;5A>>1@07=>AB8. #@>609=>ABL :C:C@C7K >?@545;O5BAO A>>B25BAB2CNI8G5B0=85;8G5AB20 2K?040NI8E >A04:>2 8 A:;04K20NI8<AO B5<?5@0BC@=K< @568<. 7028A8AB8 >B A:>@>A?5;>AB8 381@84>2 :C:C@C7K <0:A84C:B82=>ABL >15A?5G8205BAO @07=K>B=>H5=85< B5A04:>2. 708A2O7L C@>609=>AB8 =04759 D8B>2 ( C) A A>G5B0=85A04:>2 ( ) 8 AC<9 0:B82=KE B5<?5@0BC@ ( t ) 70 8N;L 289 ;5A>AB5?8 !@54=53> >2>;6LO 8MDD8F85=B :>@@5;OF88 0 , 8 9 0 . $>@20=85 C@>609=>AB8 D8B>2 ( C) 2 7028A8AB8 >B :>;8G5AB20 >A04:>2 ( ) 8 AC<<K 0:B82=KE B5?8AK205BAO A;54CNI8< C@02=5=85:1 - $>@20=85 C@>609=>AB8 75;5=>9 2 :C:C@C7K 2 7028A8AB8 >B :>;8G5AB20 >A04:>2 8 AC<<K 0:B82=KE B5A=>20=88 @57C;LB0B>2 8AA;54>20=89 8 AB0B8AB8G5A:>9 >1@01>B:8 M:A?5@82;5=>, GB> =081>;LHCN @>;L 2 D>@20=88 2KA>:>?@>4C:B82=KE 03@>F5=>7>2 @0==5A?5;KE 381@84>2 :C:C@C7K 83@05B >?B85 A>G5B0=85 AC<<K 0:B82=KE B5A04:>2 70 ?5@8>4 8N;O 8 8N=O- 8N;O. D>@20=88 C@>609=>AB8 :C:C@C7K 2 @07=K5 ?5@8>4K 2535B0F88 206=CN @>;L 83@0NB >A04:8. #@02=5=85 =5;8=59=>9 A2O78, E0@0:B5@87CNI55 2708A2O7L C@>609=>AB8 75;5=>9 2 :C:C@C7K ( C) >B :>;8G5AB20 >A04:>2 ( E) 70 8N=L- 023CAB 8 284 ?>;8=><0: C = 4 8 , 2 2 + 0 , 9 9 E 0 , 0 0 3 8 E2 + 0 , 0 0 0 0 4 4 E3 ( r 2 = 0 , 5 2 5 ) ( @8A. 2 ) . 5;8=59=0O 7028A8ABL ?>:07K205B, GB> <0:A8609 D8B>@A04:>2 >B 1 8 0 4> 2 3 0 <<. E M B E D S T A T I S T I C A . G r a p h \ s E M B E D S T A T I S T I C A . G r a p h \ s 8N=L- 023CAB : 2 - $>@20=85 C@>60O 75;5=>9 2 :C:C@C7K 2 7028A8AB8 >B :>;8G5AB20 >A04:>2 $>@20=85 C@>609=>AB8 75;5=>9 2 :C:C@C7K 2 7028A8AB8 >B :>;8G5AB20 >A04:>2 70 ?5@8>4 ?8AK205BAO C@02=5=85;8=>:07K205B, GB> =081>;55 8=B5=A82=K9 ?@8@>AB D8B>15A?5G8205BAO 2K?045=85< 70 <09- 023CAB ( E) 2 0 0 2 5 0 <A04:>2. 028A8ABL C@>609=>AB8 75;5=>9 2 ( C) >B :>;8G5AB20 >A04:>2 70 :A820;0AL =5;8=59=K< C@02=5=85;55 8=B5=A82=K9 ?@8@>AB C@>609=>AB8 >B;8G5AB20 >A04:>2 70 B 2 2 0 4> 2 6 0 <2;5=0 B5A=0O 2708A2O7L ( r 2 = 0 , 9 6 5 ) ;8G5AB2>A04:>2 70 8N=L- 023CAB 8 C@>6059 2 :C:C@C7K. 0 D>@20=85 C@>609=>AB8 A@54=5A?5;KE 381@84>2 :C:C@C7K ( C) >:07K20NB 2;8O=85 >A04:8 70 ?5@8>4 8N=L- 023CAB ( E) . 5;8=59=>5 C@02=5=85 8 284: C = 9 2 , 9 8 1 , 4 6 E + 0 , 0 1 E2 0 , 0 0 0 1 9 E3 ( r 2 = 0 , 8 6 2 ) . 028A8ABL C@>609=>AB8 @0==5A?5;KE 381@84>2 ( C) >B :>;8G5AB20 >A04:>2 70 2535B0F8N ( E) ?@54AB02;5=0 C@02=5=85<: C = 8 , 0 5 + 0 , 0 0 1 3 E + 0 , 0 0 1 3 E2 0 , 0 0 0 3 0 E3 ( r 2 = 0 , 5 8 5 ) . 708A2O7L C@>609=>AB8 75;5=>9 2 ( C) >B :>;8G5AB20 >A04:>2 70 2535B0F8N ( E) E0@0:B5@87>20;0AL :>MDD8F85=B>@@5;OF88 0 , 6 6 8 . 5;8=59=>5 C@02=5=85 8 284: C = 1 2 9 , 5 2 1 , 5 1 E + 0 , 0 0 7 2 E2 0 , 0 0 0 1 E3 . $>@20=85 C@>609=>AB8 75;5=>9 2 :C:C@C7K ( C) 2 7028A8AB8 >B :>;8G5AB20 >A04:>2 70 2535B0F8N ( E) >?8AK20;>AL C@02=5=85<: C = 2 7 , 1 9 + 0 , 0 0 5 2 E + 0 , 0 0 0 5 2 E2 0 , 0 0 0 0 0 9 2 E3 ( r 2 = 0 , 6 2 0 ) . "0:81@07>;LH0O C@>609=>ABL @0==5A?5;KE 381@84>2 :C:C@C7K D>@;8G5AB25 >A04:>2 2 ?5@8>4 2535B0F88 2 6 0 - 3 0 0 <<, <0:A8<C609=>AB8 A@54=5@0==8E 381@84>2 2>76=> ?>;CG8BL ?@8 2K?045=88 3 0 0 - 3 3 0 <A04:>2. 081>;LH0O ?@>4C:B82=>ABL A@54=5A?5;KE 381@84>2 65B 1KBL ?>;CG5=0 ?@8 2K?045=88 70 2535B0F8N 1>;55 3 6 0 <A04:>2. ?@>F5AA5 D>@20=8O C@>60O 4>AB0B>G=> ?>;=CN E0@0:B5@8AB8:C CA;>289 B5?;>- 8 2;03>>15A?5G5==>AB8 ?>A52>2 405B 384@>B5@MDD8F85=B ( ") . 708A2O7L " 609=>AB8 75;5=>9 2 :C:C@C7K ( C) E0@0:B5@87>20;0AL C@02=5=85<: C = 2 5 , 7 2 + 1 0 1 , 0 3 E 4 7 , 8 3 E2 + 4 , 6 5 E3 ( r 2 = 0 , 5 5 7 ) . "0:, A C25;8G5=85 1 , 3 C@>609=>ABL 2>7@0AB05B. !2O7L <564C MB8<8 25;8G8=0<8 2 7028A8AB8 >B " 8N=O - 8N;O 0??@>:A8<8@C5BAO =5;8=59=K< C@02=5=85<: C = 2 2 , 7 1 0 , 9 2 E + 1 2 , 1 3 E2 4 , 3 0 E3 ( r 2 = 0 , 6 3 2 ) . @57C;LB0B5 3>;5B=8E 8AA;54>20=89 CAB0=>2;5=>, GB> 2 CA;>28OE ;5A>AB5?8 C @54=53> >2>;6LO ?>;CG5=85 =081>;LH59 C@>609=>AB8 75;5=>9 2 :C:C@C7K 2>76=> ?@8 " ( E) 1 , 0 - 1 , 3 70 ?5@8>4 8N=L- 023CAB ( @8A. 3 ) . 0;L=59H55 C25;8G5=85 " A=8605B ?@8@>AB D8B> 1 , 0 =0 :064K5 0 , 1 " D>@?>;=8B5;L=> 3 , 0 B/ 30. 5;8=59=>5 C@02=5=85, >?8AK20NI55 MBC 7028A8ABL, 8: 3 - $>@20=85 C@>60O 75;5=>9 2 :C:C@C7K 2 7028A8AB8 >B " ;O A@54=5@0==8E 381@84>2 <0:A8<C9 15A?5G8205BAO ?@8 " 70 8N=L- 023CAB 1 , 2 - 1 , 3 . 028A8ABL 609=>ABLN D8B>:A8<8@C5BAO C@02=5=85;LHCN C@>609=>ABL D8B>@:A89 7028A8AB8 C@02=5=85 ?@8>1@5B05B 284: y = 7 2 , 7 + 9 4 , 5 x 1 0 7 , 3 x 2 + 1 2 , 9 x 3 , ( r 2 = 0 , 7 3 2 ) ( @8A. 3 ) . 7028A8AB8 >B A:>@>A?5;>AB8 2 @07;8G=K5 ?5@8>4K 2535B0F88 381@84K :C:C@C7K ?@54JO2;ONB =5>48=0:>2K5 B@51>20=8O : @568AB8. =0;87 3>;5B=8E M:A?5@81@01>B:0 ?>72>;8;8 2KO28BL ?>;>68B5;L=CN 2708A2O7L C@>609=>AB8 @0==5A?5;KE 381@84>2 :C:C@C7K ( z ) A 70?0A04C:B82=>9 2;038 2 2>5 ?>G2K ?5@54 ?>A52>;8G5AB2>A04:>2 ( E) 70 8N=L- 023CAB. ;O 3@C??K @0==5A?5;KE 381@84>2 >=0 >?8AK205BAO C@02=5=852 C@02=5=85 8 284: Z = 1 1 2 6 , 2 + 0 , 0 8 2 E 1 , 4 8 C 0 , 0 0 1 8 E2 + 0 , 0 0 5 9 EC + 0 , 0 0 4 1 C2 ( r 2 = 0 , 6 2 1 ) . #AB0=>2;5=>, GB> C25;8G5=85 :>;8G5AB20 4>ABC?=>9 2;038 ( E) A 2 4 0 4> 3 6 0 <4 A 023CAB A?>A>1AB2>20;> @>ABC C@>609=>AB8 ( C) @0==5A?5;KE 381@84>2 A 2 8 , 0 4> 4 0 B/ 30, B> 5ABL =0 :064K5 1 0 <ABC?=>9 2;038 4>?>;=8B5;L=> D>@9 <0AAK. -B0 7028A8ABL 0??@>:A8<8@C5BAO =5;8=59=K< C@02=5=85 2840: C = 2 4 7 , 3 6 2 , 3 3 E + 0 , 0 0 8 0 E2 0 , 0 0 0 0 8 6 E3 ( r 2 = 0 , 5 6 9 ) . D>@20=88 D8B>2 ( C) 7=0G8B5;L=CN @>;L 83@05B :>;8G5AB2> 4>ABC?=>9 2;038 2 B5G5=85 8N=O- 023CAB0 ( E) . 081>;LH89 ?@8@>AB 18>B70?0A>2 >B 2 4 0 4> 3 8 0 <<, =0G8=0O A 2 4 0 <<, =0 :064K5 1 0 <@?>;=8B5;L=> 2 , 5 B/ 30 75;5=>9 <0AAK. -B0 7028A8ABL 0??@>:A8<8@C5BAO C@02=5=852 =5;8=59=0O 7028A8ABL <564C =0;8G85ABC?=>9 2;038 70 8N=L- 023CAB ( E) 8 C@>609=>ABLN 75;5=>9 :A820;0AL C@02=5=852 @>;L 4>ABC?=>9 2;038 8N;O- 023CAB0 1>;55 7=0G8B5;L=0, G5< 4;O @0==5A?5;KE. "0:, 2708A2O7L :>;8G5AB20 4>ABC?=>9 2;038 70 ?5@8>4 2535B0F88 A 8N;O ?> 023CAB ( E) 8 C@>6059 2 :C:C@C7K ( C) 0??@>:A8<8@C5BAO C@02=5=85;8=><0 B@5BL59 AB5?5=8: C = 1 1 6 0 , 0 4 1 5 , 4 5 E + 0 , 0 6 9 E2 0 , 0 0 1 0 E3 ( r 2 = 0 , 5 7 1 ) . 028A8ABL C@>609=>AB8 75;5=>9 2 :C:C@C7K ( C) >B :>;8G5AB20 4>ABC?=>9 2;038 ( E) 70 8N=L- 023CAB 8BK 7028A8AB8 C@>609=>AB8 75;5=>9 2 ( C) >B :>;8G5AB20 4>ABC?=>9 2;038 70 8N;L- 023CAB ( E) E0@0:B5@87>20;0AL :>MDD8F85=B>@@5;OF88 0 , 6 7 7 , 0 C@02=5=85 8 284: C = - 1 0 8 5 , 5 + 1 4 , 4 6 E 0 , 0 6 2 E2 + 0 , 0 0 0 8 7 E3 ( r 2 = 0 , 6 7 7 ) . =0;87 ?>3>4=KE CA;>289 70 1 9
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