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V= 0,114/17,10*100% = 0,67%, < 30%, 7=0G8B, A@54=OO 25;8G8=0 AG8B05BAO =0456=>9. !@54=OO >H81:0 2K1>@:8:  EMBED Equation.3   EMBED Equation.3  @545;L=0O >H81:0 2K1>@:8 4;O A@54=59 (D0:B8G5A:>5 @0AE>645=85 <564C 2K1>@>G=>9 A@54=59 8 35=5@0;L=>9) (?@8 15A?>2B>@=>< >B1>@5):  EMBED Equation.3  @545;L=0O >B=>A8B5;L=0O >H81:0 2K1>@:8 (4;O A@54=59):  EMBED Equation.3 = 0,032/17,10*100 =0,19% >AG8B02 =5>1E>48<K5 7=0G5=8O, ?@>25@8< ?@028;L=>ABL 2K1@0==>9 A>2>:C?=>AB8:  EMBED Equation.3   EMBED Equation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x 8 y. > E0@0:B5@C @0A?>;>65=8O B>G5: =0 ?>;5 :>@@5;OF88 45;0NB 2K2>4 > =0;8G88 8;8 >BACBAB288 A2O78, > E0@0:B5@5 A2O78. F5=:0 A2O78 <564C :>;8G5AB25==K<8 ?@87=0:0<8. "5A=>B0 A2O78 <564C :>;8G5AB25==K<8 ?@87=0:0<8 >?@545;O5BAO ?> A;54CNI8< ?>:070B5;O<: M<?8@8G5A:>5 :>@@5;OF8>==>5 >B=>H5=85; ?0@=K9 :>MDD8F85=B :>@@5;OF88. 0@=K9 :>MDD8F85=B :>@@5;OF88 E0@0:B5@87C5B B5A=>BC 8 =0?@02;5=85 A2O78 <564C :>@@5;8@C5<K<8 ?@87=0:0<8 2 A;CG05 =0;8G8O <564C =8<8 ;8=59=>9 7028A8<>AB8:  EMBED Equation.3 , 345 a  :>MDD8F85=B @53@5AA88 2 C@02=5=88 A2O78,  EMBED Equation.3 - A@54=5:204@0B8G5A:85 >B:;>=5=8O A>>B25BAB2CNI53> D0:B>@=>3> 8 @57C;LB0B82=>3> ?@87=0:>2. ! ?><>ILN DC=:F88    @0AAG8BK205BAO :>MDD8F85=B ?0@=>9 :>@@5;OF88 <564C 8AA;54C5<K<8 ?@87=0:0<8. @8 %r%< 0,3, B> A2O7L <564C ?@87=0:0<8 ?@0:B8G5A:8 >BACBAB2C5B, 0,3<%r%< 0,5  A2O7L A;010O, ?@8 %r%= 0,5-0,7  C<5@5==0O, ?@8 %r%>0,7  A8;L=0O (B5A=0O). F5=:0 7=0G8<>AB8 :>MDD8F85=B0 :>@@5;OF88, 8A?>;L7CO t-:@8B5@89 !BLN45=B0. @>2>48< >F5=:C 7=0G8<>AB8 :>MDD8F85=B0 :>@@5;OF88:  EMBED Equation.3 , 345 (n-2)  G8A;> AB5?5=59 A2>1>4K ?@8 7040==>< C@>2=5 7=0G8<>AB8 0 8 >1JQ<5 2K1>@:8 n. >;CG5==>5 7=0G5=85  EMBED Equation.3 A@02=8205< A B01;8G=K< 7=0G5=85< t-:@8B5@8O (4;O 0=0,05). A;8  EMBED Equation.3 1>;LH5  EMBED Equation.3  ;8=59=K9 :>MDD8F85=B AG8B05BAO 7=0G8<K<, 0 A2O7L <564C E 8 C ACI5AB25==>9. A;8  EMBED Equation.3 <5=LH5  EMBED Equation.3  ;8=59=K9 :>MDD8F85=B AG8B05BAO =57=0G8<K<, 0 A2O7L <564C E 8 C >BACBAB2C5B.  40==>9 @01>B5  EMBED Equation.3  ?@8 G8A;5 AB5?5=59 A2>1>4K (n-2) = 50-2=48 8 0=0,05.  40==>9 @01>B5 <K >F5=820;8 A2O7L <564C C@>2=5< CA?5205<>AB8 ABC45=B>2 ;048<8@A:>3> 07>2>3> 548F8=A:>3> >;;5460, 8E ?>A5I05<>ABLN, ?@5>1;040NI59 >F5=:>9 2 0BB5AB0B5 (?@8;>65=85 3 ). !2O7L <564C >F5=:>9, ?@5>1;040NI59 2 0BB5AB0B5 ABC45=B>2 8 C@>2=5< 8E CA?5205<>AB8. 0 >A=>25 40==KE ?@8;>65=8O 3 AB@>8< ?>;5 @0AA5820=8O 7=0G5=89, 8A?>;L7CO ?@>3@0<<C Microsoft Excel.  8A.1 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2  >B >F5=:8, ?@5>1;040NI59 2 8E 0BB5AB0B5. - ?0@=K9 :>MDD8F85=B :>@@5;OF88.  EMBED Equation.3 , "0: :0: %r%= 0,823, 0,823>0,7, 7=0G8B, A2O7L A8;L=0O. - F5=:0 7=0G8<>AB8 :>MDD8F85=B0 :>@@5;OF88, 8A?>;L7CO t-:@8B5@89 !BLN45=B0.  EMBED Equation.3 >2,0106. "0: :0:  EMBED Equation.3 >  EMBED Equation.3 , 7=0G8B, ;8=59=K9 :>MDD8F85=B AG8B05BAO 7=0G8<K<, 0 A2O7L <564C E 8 C ACI5AB25==>9. !2O7L <564C ?>A5I05<>ABLN ABC45=B>2 8 C@>2=5< 8E CA?5205<>AB8. 0 >A=>25 40==KE ?@8;>65=8O 3 AB@>8< ?>;5 @0AA5820=8O 7=0G5=89, 8A?>;L7CO ?@>3@0<<C Microsoft Excel.  8A.2 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2  >B 8E ?>A5I05<>AB8 CG51=KE 8 ?@0:B8G5A:8E 70=OB89. - ?0@=K9 :>MDD8F85=B :>@@5;OF88.  EMBED Equation.3  "0: :0: %r%= 0,547, 0,5<0,547<0,7, 7=0G8B, A2O7L C<5@5==0O. - F5=:0 7=0G8<>AB8 :>MDD8F85=B0 :>@@5;OF88, 8A?>;L7CO t-:@8B5@89 !BLN45=B0.  EMBED Equation.3 >2,0106 "0: :0:  EMBED Equation.3 >  EMBED Equation.3  ,7=0G8B, ;8=59=K9 :>MDD8F85=B AG8B05BAO 7=0G8<K<, 0 A2O7L <564C E 8 C ACI5AB25==>9. $>@<8@>20=85 <>45;8 ?0@=>9 @53@5AA88 0@=0O @53@5AA8O E0@0:B5@87C5B A2O7L <564C 42C<O ?@87=0:0<8: @57C;LB0B82=K< 8 D0:B>@=K<. >@O4>: D>@<8@>20=8O <>45;8 ?0@=>9 @53@5AA88: AA;54C5BAO 3@0D8G5A:0O 7028A8<>ABL 42CE ?@87=0:>2. ACI5AB2;O5BAO >F5=:0 ?0@0<5B@>2 <>45;8 @53@5AA88. @>872>48BAO ?@>25@:0 ?>;CG5==>9 <>45;8 =0 045:20B=>ABL. A;8 87CG05BAO A2O7L <564C 42C<O ?5@5<5==K<8, ?@8G5< 8E <>6=> @0AA<0B@820BL :0: D0:B>@ 8 @57C;LB0B, B> MBC 7028A8<>ABL F5;5A>>1@07=> ?@54AB028BL 2 <0B5<0B8G5A:>< 2845. ! MB>9 F5;LN ?>418@0NB DC=:F8N y=f(x), :>B>@0O =08;CGH8< >1@07>< A>>B25BAB2C5B 8AE>4=K< 40==K<, B.5. >15A?5G8205B =08;CGHCN 0??@>:A8<0F8N ?>;O :>@@5;OF88. 0B5<0B8G5A:>5 >?8A0=85 7028A8<>AB8 2 A@54=5< 87<5=5=89 ?5@5<5==>9 y >B ?5@5<5==>9 x =07K205BAO C@02=5=85< ?0@=>9 @53@5AA88. -B> C@02=5=85 <>6=> ?>;CG8BL ?@8 ?><>I8 Microsoft Excel. @>2>48< >F5=:C 40==>9 <>45;8 =0 045:20B=>ABL: =0G5=85 A@54=59 >H81:8 0??@>:A8<0F88: 0,0241 ?@545;O5< 7=0G8<>ABL :>MDD8F85=B>2 A ?><>ILN t-:@8B5@8O !BLN45=B0.  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  - A@54=55 :204@0B8G5A:>5 >B:;>=5=85 D0:B>@=>3> ?@87=0:0 x >B >1I59 A@54=59  EMBED Equation.3 . ;O ?@>2545=8O @53@5AA8>==>3> 0=0;870 @0AAG8BK20NB 4>?>;=8B5;L=25 ?>:070B5;8: >MDD8F85=B M;0AB8G=>AB8, ?>:07K20NI89 GC2AB28B5;L=>ABL @57C;LB0B82=>3> ?@87=0:0 : 87<5=5=8N D0:B>@=>3>:  EMBED Equation.3 , 345  EMBED Equation.3  - A@54=55 7=0G5=85 A>>B25BAB25==> D0:B>@=>3> 8 @57C;LB0B82=>3> ?@87=0:0. >MDD8F85=B M;0AB8G=>AB8 ?>:07K205B, =0 A:>;L:> ?@>F5=B>2 2 A@54=5< 87<5=8BAO 7=0G5=85 @57C;LB0B82=>3> ?@87=0:0 ?@8 87<5=5=88 D0:B>@=>3> ?@87=0:0 =0 1%. >MDD8F85=B 45B5@<8=0F88, :>B>@K9 >F5=8205B 7028A8<>ABL 20@80F88 @57C;LB0B82=>3> ?@87=0:0:  EMBED Equation.3  , 345  EMBED Equation.3 - A@54=5:204@0B8G=>5 >B:;>=5=85 A>>B25BAB25==> D0:B>@=>3> 8 @57C;LB0B82=>3> ?@87=0:0.  EMBED Equation.3  - ?0@=K9 :>MDD8F85=B :>@@5;OF88 <564C @57C;LB0B82=K< 8 D0:B>@=K< ?@87=0:0<8. >MDD8F85=B 45B5@<8=0F88 ?@8=8<05B 7=0G5=85 2 8=B5@20;5 (0,1). '5< 1;865 7=0G5=85 : 1, B5< B5A=55 A2O7L. "0:65 :>MDD8F85=B 45B5@<8=0F88 <>65B 1KBL 2K@065= 2 %. 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2 >B >F5=:8, ?@5>1;040NI59 2 8E 0BB5AB0B5. 0 >A=>25 40==KE ?@8;>65=8O 3 AB@>8< ?>;5 @0AA5820=8O 7=0G5=89, 8A?>;L7CO ?@>3@0<<C Microsoft Excel.  8A. 3 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2  >B >F5=:8, ?@5>1;040NI59 2 8E 0BB5AB0B5. 028A8<>ABL 2K@0605BAO C@02=5=85< y=2,9223x+4,8849, 45 C  M:70<5=0F8>==K9 10;;, %  >F5=:0, ?@5>1;040NI0O 2 0BB5AB0B5. @>254Q< >F5=:C 40==>9 <>45;8 =0 045:20B=>ABL: =0G5=85 A@54=59 >H81:8 0??@>:A8<0F88: 0,6781 ?@545;O5< 7=0G8<>ABL :>MDD8F85=B>2 A ?><>ILN t-:@8B5@8O !BLN45=B0.  EMBED Equation.3  = 1,04  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  8  EMBED Equation.3 , 7=0G8B, >10 ?0@0<5B@0 ?@87=0NBAO 7=0G8<K<8, GB> 3>2>@8B > B5A=>9 A2O78 <564C ?@87=0:0<8.  EMBED Equation.3  0 >A=>25 ?>;CG5==>3> :>MDD8F85=B0 M;0AB8G=>AB8, @02=>3> 0,71%, <>6=> A45;0BL 2K2>4 > B><, GB> ?@8 87<5=5=88 0BB5AB0F8>==>9 >F5=:8 ABC45=B0 =0 1%, 53> C@>25=L CA?5205<>AB8 87<5=8BAO =0 71%.  EMBED Equation.3  =0G5=85 @0AAG8B0==>3> :>MDD8F85=B0 45B5@<8=0F88 ?>:07K205B, GB> CA?5205<>ABL ABC45=B>2 7028A8B >B A@54=59 0BB5AB0F8>==>9 >F5=:8 ABC45=B>2 =0 68,6%. 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2 >B 8E ?>A5I05<>AB8. 0 >A=>25 40==KE ?@8;>65=8O 3 AB@>8< ?>;5 @0AA5820=8O 7=0G5=89, 8A?>;L7CO ?@>3@0<<C Microsoft Excel.  8A. 4 028A8<>ABL C@>2=O CA?5205<>AB8 ABC45=B>2  >B 8E ?>A5I05<>AB8. 028A8<>ABL 2K@0605BAO C@02=5=85< y=0,1722x + 0,5047, 45 C  M:70<5=0F8>==K9 10;;, %  ?>A5I05<>ABL, %. @>254Q< >F5=:C 40==>9 <>45;8 =0 045:20B=>ABL: =0G5=85 A@54=59 >H81:8 0??@>:A8<0F88: 0,2993 ?@545;O5< 7=0G8<>ABL :>MDD8F85=B>2 A ?><>ILN t-:@8B5@8O !BLN45=B0.  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Microsoft Excel A>740;8 B01;8FC A 8AE>4=K<8 40==K<8 (?@8;>65=85 3) 8 >B:@K;8 53> G5@57 Statgrafics Plus. K720;8 ?@>3@0<<C <=>65AB25==>9 @53@5AA88 Multiple Regression.  >:=5 Dependent Variable C:07K205< 3@0DC, A>45@60ICN 40==K5 @57C;LB0B82=>3> ?@87=0:0.  >:=5 Independent Variable 70?8AK205< 3@0DK A D0:B>@=K<8 ?@87=0:0<8, 70?CA:05< ?@>3@0<<C. >;CG05< A;54CNI85 40==K5. Multiple Regression Analysis ----------------------------------------------------------------------------- Dependent variable: Col_5 ----------------------------------------------------------------------------- Standard T Parameter Estimate Error Statistic P-Value ----------------------------------------------------------------------------- CONSTANT 10,6587 2,46537 4,32335 0,0001 Col_1 1,14481 0,196915 5,81372 0,0000 Col_2 0,052846 0,0745219 0,709133 0,4819 Col_3 0,593339 0,481694 1,23178 0,2244 Col_4 - 0,00601097 0,0254667 -0,236033 0,8145 ----------------------------------------------------------------------------- Analysis of Variance ----------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value ----------------------------------------------------------------------------- Model 138,491 4 34,6227 51,92 0,0000 Residual 30,0094 45 0,666874 ----------------------------------------------------------------------------- Total (Corr.) 168,5 49 R-squared = 82,1903 percent R-squared (adjusted for d.f.) = 80,6072 percent Standard Error of Est. = 0,816624 Mean absolute error = 0,5729 Durbin-Watson statistic = 1,89771 The StatAdvisor --------------- The output shows the results of fitting a multiple linear regression model to describe the relationship between Col_5 and 4 independent variables. The equation of the fitted model is Col_5 = 10,6587 + 1,14481*Col_1 + 0,052846*Col_2 + 0,593339*Col_3 - 0,00601097*Col_4 Since the P-value in the ANOVA table is less than 0.01, there is a statistically significant relationship between the variables at the 99% confidence level. The R-Squared statistic indicates that the model as fitted explains 82,1903% of the variability in Col_5. The adjusted R-squared statistic, which is more suitable for comparing models with different numbers of independent variables, is 80,6072%. The standard error of the estimate shows the standard deviation of the residuals to be 0,816624. This value can be used to construct prediction limits for new observations by selecting the Reports option from the text menu. The mean absolute error (MAE) of 0,5729 is the average value of the residuals. The Durbin-Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the DW value is greater than 1.4, there is probably not any serious autocorrelation in the residuals. In determining whether the model can be simplified, notice that the highest P-value on the independent variables is 0,8145, belonging to Col_4. Since the P-value is greater or equal to 0.10, that term is not statistically significant at the 90% or higher confidence level. Consequently, you should consider removing Col_4 from the model. "01;8F0 2. 57C;LB0BK 0=0;870 <=>65AB25==>9 @53@5AA88. 0@0<5B@K=0G5=85 ?0@0<5B@>2!B0B8AB8:0 4;O >BA520 =57=0G8<KE D0:B>@>2, @57C;LB0BK 48A?5@A8>==>3> 0=0;870!B0=40@B=>5 >B:;>=5=85@5<O =0 ?>43>B>2:C : CG51=K< 8 ?@0:B8G5A:8< 70=OB8O< (col 1)1,144815,813720,0000>7@0AB (col 2)0,0528460,7091330,4819F5=:0, ?@5>1;040NI0O 2 0BB5AB0B5 (col 3)0,5933391,231780,2244>A5I05<>ABL (col 4)- 0,00601097-0,2360330,8145"0:8< >1@07><, ?>;CG05< A;54CNI55 C@02=5=85 <=>65AB25==>9 @53@5AA88: col_5 = 10,6587 +1,14481 *col_1 + 0,052846*col_2 + 0,593339*col_3 - 0,00601097*col_4. >45;L AG8B05BAO 045:20B=>9, 5A;8 R-squared = 70%. K ?>;CG8;8 R-squared = 82,1903%. 0==K9 @57C;LB0B <>65B 1KBL ?@87=0= 4>2>;L=> 1;87:8< : B@51C5<><C 8 <>3 1KBL ?>;CG5= 2A;54AB285 B>3>, GB> =081>;LH55 2;8O=85 =0 CA?5205<>ABL >:07K20NB D0:B>@K, :>B>@K5 =52>7<>6=> ?@54AB028BL 2 :>;8G5AB25==>9 D>@<5. F5=:0 045:20B=>AB8 <>45;8 <=>65AB25==>9 @53@5AA88 45:20B=>AB8 <>45;8 ?@>25@O5BAO A ?><>ILN ?@>3@0<<=KE A@54AB2 Microsoft Excel. ;O ?>AB@>5=8O ;8=59=>9 @53@5AA8>==>9 <>45;8 =5>1E>48<>: ?>43>B>28BL A?8A>: 87 AB@>:8 AB>;1F>2 (?@8;>65=85 3), A>45@60I89 M:A?5@8<5=B0;L=K5 40==K5 (AB>;15F, A>45@60I89 2KE>4=CN 25;8G8=C C 4>;65= 1KBL ;81> ?5@2K<, ;81> ?>A;54=8< 2 A?8A:5); >1@0B8BLAO : <5=N !5@28A/=0;87 40==KE/ 53@5AA8O 2 480;>3>2>< >:=5 53@5AA8O 7040BL: 2E>4=>9 8=B5@20; Y; 2E>4=>9 8=B5@20; X; 2KE>4=>9 8=B5@20;  OG59:0, 2 :>B>@>9 1C4CB ?><5I0BLAO @57C;LB0BK 2KG5A;5=89 =060BL  8 ?@>0=0;878@>20BL @57C;LB0BK. >;CG05< A;54CNI85 40==K5: + " 53@5AA8>==0O AB0B8AB8:0=>65AB25==K9 R0,90658864R-:204@0B0,82190296>@<8@>20==K9 R-:204@0B0,80607212!B0=40@B=0O >H81:00,8166238201;N45=8O508A?5@A8>==K9 0=0;87dfSSMSF=0G8<>ABL F 53@5AA8O4138,4906534,62266251,917811542,689E-16AB0B>:4530,0093510,6668745B>3>49168,5>MDD8F85=BK!B0=40@B=0O >H81:0t-AB0B8AB8:0P-=0G5=8586=85 95%5@E=85 95%86=85 95,0%5@E=85 95,0%Y-?5@5A5G5=8510,65865052,46536834,32335018,40611E-055,693143815,6241575,693143815,624157@5<O =0 ?>43>B>2:C : CG51=K< 8 ?@0:B.70=OB8O<1,144807720,19691485,81372235,89772E-070,7482011,54141440,7482011,5414144>7@0AB0,052845960,07452190,70913320,481899869-0,09724890,2029408-0,09724890,2029408F5=:0, ?@5>1;. 2 0BB5AB0B50,593339060,48169361,2317770,224430513-0,37684161,5635197-0,37684161,5635197>A5I05<>ABL-0,0060110,0254667-0,2360330,814478271-0,05730350,0452816-0,05730350,0452816 7 0=0;870 <=>65AB25==>9 @53@5AA88 284=>, GB>  EMBED Equation.3 =51,92. 5;8G8=0  EMBED Equation.3  =0E>48BAO ?> B01;8F0< ?@8 7040==>< C@>2=5 7=0G8<>AB8  EMBED Equation.3  (0,05) 8 G8A;5 AB5?5=59 A2>1>4K  EMBED Equation.3  = 4-1 = 3;  EMBED Equation.3  = 50-4 = 46. "0:8< >1@07><,  EMBED Equation.3 =2,8<51,92.  EMBED Equation.3 > EMBED Equation.3 , 7=0G8B, A2O7L ?@87=05BAO <564C ?@87=0:0<8 ?@87=05BAO ACI5AB25==>9 8 38?>B570 > =5A>>B25BAB288 70;>65==KE 2 C@02=5=85 @53@5AA88 A2O759 @50;L=> ACI5AB2CNI8< >B25@305BAO. F5=:0 2;8O=8O D0:B>@=KE ?@87=0:>2 =0 @57C;LB8@CNI89 =>65AB25==K9 :>MDD8F85=B :>@@5;OF88 E0@0:B5@87C5B B5A=>BC 8 =0?@02;5=85 A2O78 <564C D0:B>@=K<8 ?@87=0:0<8 8 @57C;LB8@CNI8< 2 A;CG05 =0;8G8O <564C =8<8 ;8=59=>9 7028A8<>AB8. @8 %r%< 0,3, B> A2O7L <564C ?@87=0:0<8 ?@0:B8G5A:8 >BACBAB2C5B, 0,3<%r%< 0,5  A2O7L A;010O, ?@8 %r%= 0,5-0,7  C<5@5==0O, ?@8 %r%>0,7  A8;L=0O (B5A=0O). =>65AB25==K9 :>MDD8F85=B 45B5@<8=0F88 >F5=8205B 7028A8<>ABL 20@80F88 @57C;LB0B82=>3> ?@87=0:0. >MDD8F85=B 45B5@<8=0F88 ?@8=8<05B 7=0G5=85 2 8=B5@20;5 (0,1). '5< 1;865 7=0G5=85 : 1, B5< B5A=55 A2O7L. "0:65 :>MDD8F85=B 45B5@<8=0F88 <>65B 1KBL 2K@065= 2 %. AE>4O 87 0=0;870 <=>65AB25==>9 @53@5AA88, <=>65AB25==K9 :>MDD8F85=B :>@@5;OF88 @025= 0,9066, 7=0G8B, <564C ?@87=0:0<8 A8;L=0O A2O7L. =0G5=85 @0AAG8B0==>3> :>MDD8F85=B0 45B5@<8=0F88 0,8219 ?>:07K205B, GB> C@>25=L CA?5205<>AB8 ABC45=B>2 7028A8B >B B0:8E D0:B>@=KE ?@87=0:>2, :0: 2@5<O, C45;O5<>5 2K?>;=5=8N 4><0H=53> 7040=8O, 2>7@0AB ABC45=B0, 53> ?>A5I05<>ABL 8 >F5=:0, ?@5>1;040NI0O 2 0BB5AB0B5, =0 82,19%. F5=:0 2708<>A2O78 <564C :0G5AB25==K<8 ?@87=0:0<8 F5=:0 2708<>A2O78 <564C 20@80F8>==K<8 ?@87=0:0<8 F5=:0 =5:>B>@KE A>F80;L=KE O2;5=89 >A;>6=O5BAO B5<, GB> <=>385 87 =8E =5 8<5NB :>;8G5AB25==>9 >F5=:8. ;O MB>3> ?@8<5=ONBAO =5?0@0<5B@8G5A:85 <5B>4K, A ?><>ILN :>B>@KE CAB0=02;8205BAO A2O7L <564C :0G5AB25==K<8 (0B@81CB82=K<8) ?@87=0:0<8. B@81CB82=K5 ?@87=0:8 =5 ?>440NBAO :>;8G5AB25==><C 2K@065=8N, ?>MB><C ?@8 87CG5=88 A2O78 <564C :0G5AB25==K<8 ?@87=0:0<8 =5 AB028BAO 7040G0 ?@54AB02;5=8O 5Q C@02=5=85<. 45AL @5GL 84QB >1 CAB0=>2;5=88 =0;8G8O A2O78 8 87<5@5=8O 5Q B5A=>BK. ;O MB>3> ?@8<5=ONBAO :>MDD8F85=BK 0AA>F80F88 8 :>=B8=35=F88. @8 8AA;54>20=88 A2O78 G8A;>2>9 <0B5@80; @0A?>;030NB 2 2845 B01;8F A>?@O65==>AB8: aba+bcdc+da+cb+da+b+c+d >MDD8F85=B 0AA>F80F88:  EMBED Equation.3  >MDD8F85=B :>=B8=35=F88:  EMBED Equation.3  =0G5=8O :>MDD8F85=B>2 87<5=ONBAO >B -1 4> +1; G5< 1;865 : +1 8;8 : -1, B5< A8;L=55 A2O70=K <564C A>1>9 87CG05<K5 ?@87=0:8. >MDD8F85=B :>=B8=35=F88 2A5340 <5=LH5 :>MDD8F85=B0 0AA>F80F88. !2O7L <564C ?@87=0:0<8 AG8B05BAO ?>4B25@645==>9, 5A;8  EMBED Equation.3 8;8  EMBED Equation.3 . A;8 :064K9 87 :0G5AB25==KE ?@87=0:>2 A>AB>8B 1>;55, G5< 8E 2-E 3@C??, B> 4;O >?@545;5=8O B5A=>BK A2O78 2>7<>6=> ?@8<5=5=85 :>MDD8F85=B0 2708<=>9 A>?@O65==>AB8 8@A>=0-'C?@>20. >MDD8F85=B 8@A>=0:  EMBED Equation.3  >MDD8F85=B 'C?@>20:  EMBED Equation.3 , 345  EMBED Equation.3  - ?>:070B5;L 2708<=>9 A>?@O65==>AB8, >?@545;O5BAO :0: AC<<0 :204@0B>2 G0AB>B :064>9 :;5B:8 B01;8FK : ?@>872545=8N 8B>3>2KE G0AB>B A>>B25BAB2CNI53> AB>;1F0 8 AB@>:8. KG8B0O 87 MB>9 AC<<K 1 ?>;CG8< =C6=CN 25;8G8=C.  EMBED Equation.3 -1; 1  G8A;> 7=0G5=89 (3@C??) ?5@2>3> ?@87=0:0; 2 - G8A;> 7=0G5=89 (3@C??) 2B>@>3> ?@87=0:0. '5< MB8 :>MDD8F85=BK 1;865 : 1, B5< A2O7L B5A=55.  EMBED Equation.3  ;O @0AG5B0 :>MDD8F85=B0 2708<=>9 A>?@O65==>AB8 AB@>8BAO B01;8F0: y2A53>123x1 EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 2 EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 3 EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 8B>3> EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3   40==>9 @01>B5 ?@>2>48;0AL >F5=:0 2708<>A2O78 A;54CNI8E :0G5AB25==KE ?@87=0:>2: F5;L ?>ABC?;5=8O 2 ; A5<59=>5 ?>;>65=85; =0;8G85 @01>BK; CG0AB85 2 ?@0:B8G5A:8E <548F8=A:8E 70=OB8OE; C3;C1;5==>ABL ?>43>B>2:8.  @57C;LB8@CNI53> ?@87=0:0  CA?5205<>AB8 ABC45=B>2. !@54=55 7=0G5=85 @57C;LB8@CNI53> ?@87=0:0:  EMBED Equation.3 =17,1 @5>1@07>20=85 @57C;LB8@CNI53> (:>;8G5AB25==>3>) ?@87=0:0 2 :0G5AB25==K9: -:70<5=0F8>==K9 10;;!-61-58$-482A53>%KH5 A@54=53>7982448865 A@54=53>96112652 708<>A2O7L F5;8 ?>ABC?;5=8O 2 :>;;546 ABC45=B>2 8 C@>2=O 8E CA?5205<>AB8. &5;L ?>ABC?;5=8O ABC45=B0 2 :>;;5462A53>>;CG8BL ?@>D5AA8N>;CG8BL 48?;><0 MB>< =0AB>O;8 @>48B5;8-:70<5=0F8>==K9 10;;KH5 A@54=53>210021865 A@54=53>16112292A53>3711250 A;8 :064K9 87 >48= :0G5AB25==KE ?@87=0:>2 A>AB>8B 1>;55, G5< 87 2-E 3@C??, B> 4;O >?@545;5=8O B5A=>BK A2O78 2>7<>6=> ?@8<5=5=85 :>MDD8F85=B0 2708<=>9 A>?@O65==>AB8 8@A>=0-'C?@>20.  EMBED Equation.3 =(441/(37*21))+(0/(11*21))+(0/(2*21))+(256/(37*29))+(121/(11*29))+(4/(2* *29))-1 = 0,254  EMBED Equation.3 =0,45  EMBED Equation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quation.3 = -0,21  EMBED Equation.3  >MDD8F85=B :>=B8=35=F88 <5=LH5 :>MDD8F85=B0 0AA>F80F88. !2O7L <564C ?@87=0:0<8 <>6=> AG8B0BL ?>4B25@645==>9, => A;01>9, B.:.  EMBED Equation.3 , =>  EMBED Equation.3 . 708<>A2O7L CG0AB8O ABC45=B>2 2 >1I5AB25==>9 8 B2>@G5A:>9 687=8  8 C@>2=O 8E CA?5205<>AB8. K CG0AB2C5B5 2 A>F80;L=>->1I5AB25==>9 687=8 :>;;5460?2A53>40=5B-:70<5=0F8>==K9 10;;KH5 A@54=53>111021865 A@54=53>1712292A53>282250 AA;54C5<K5 :0G5AB25==K5 ?@87=0:8 A>AB>OB 87 2-E 3@C??, B.5. O2;ONBAO 0;LB5@=0B82=K<8, ?>MB><C 4;O 8AA;54>20=8O 7028A8<>AB8 =094Q< :>MDD8F85=B 0AA>F80F88 8 :>=B8=35=F88.  EMBED Equation.3 = -0,126  EMBED Equation.3  >MDD8F85=B :>=B8=35=F88 <5=LH5 :>MDD8F85=B0 0AA>F80F88. !2O7L <564C ?@87=0:0<8 =5;L7O AG8B0BL ?>4B25@645==>9, B.:.  EMBED Equation.3 8 EMBED Equation.3 . 708<>A2O7L ?>A5I5=8O ABC45=B0<8 181;8>B5: 8 G8B0;L=KE 70;>2 8 C@>2=O 8E CA?5205<>AB8.  K G0AB> 8A?>;L7C5B5 ?@8 ?>43>B>2:5 : CG51=K< 8 ?@0:B8G5A:8< 70=OB8O< 4>?>;=8B5;L=CN =0CG=CN ;8B5@0BC@C 8;8 =B5@=5B?2A53>40=5B-:70<5=0F8>==K9 10;;KH5 A@54=53>21021865 A@54=53>1514292A53>361450 AA;54C5<K5 :0G5AB25==K5 ?@87=0:8 A>AB>OB 87 2-E 3@C??, B.5. O2;ONBAO 0;LB5@=0B82=K<8, ?>MB><C 4;O 8AA;54>20=8O 7028A8<>AB8 =094Q< :>MDD8F85=B 0AA>F80F88 8 :>=B8=35=F88.  EMBED Equation.3 = 1  EMBED Equation.3  >MDD8F85=B :>=B8=35=F88 <5=LH5 :>MDD8F85=B0 0AA>F80F88. !2O7L <564C ?@87=0:0<8 <>6=> AG8B0BL ?>4B25@645==>9, B.:.  EMBED Equation.3 8 EMBED Equation.3 . 1I89 2K2>4 ?> @57C;LB0B0< 2K?>;=5=8O :C@A>2>9 @01>BK &5;L :C@A>2>9 @01>BK 4>AB83=CB0. 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