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????. ???????????? ?????????? ????????????? ??????????????? ???????????? ???????????? ?????????????? ???????????? . ????. 14.1 ??????14.2 ????????14.3 ????????????

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    1. ???? ???????????????

    2. ???? ???????????? ?????????? ????????????? ??????????????? ???????????? ???????????? ?????????????? ????????????

    3. ???? 14.1 ?????? 14.2 ???????? 14.3 ????????????—????? 14.4 ????????? 14.5 ???????? 14.6 ??????????????? 14.7 ????

    4. 14.1 ?????? 14.1.1 ??????? 14.1.2 ??????? 14.1.3 ??????? 14.1.4 ???????

    5. 14.1 ??????(?) ????(correlation analysis) ????????????????????,????(covariance)?????????????????????? ????????????????(dependent variable)????(?????)(independent variable)?,??????????????????;???????????,?????????????????????

    6. 14.1.1 ??????? ????(covariance) ??????????????? ???? ????????,?????????????????

    7. 14.1.1???????(?) ?????? ??N??????? ?????? ??n??????

    8. 14.1.1???????(?1) ??????? ????????-?????? X?Y????????,??X?Y?????? X?Y????????,??X?Y?????? X?Y????????,??????????????,??????????????????

    9. 14.1.1???????(?3) ??????????????,?????????????????,??????????????,????????? (??14.1????) ??????????????,?????????????????,??????????????,?????????(??14.1????) ??????????????,???????????????,??????????????,?????????????? (??14.1?????)

    10. 14.1.1???????(?2) ?14.1:??????????X?Y????

    11. ?14.1 ??????????? ??????????????????????,?????10????????14.1 ?14.1 10????????????

    12. ??14.1 ??14.1??

    13. 14.1.2 ??????? ????(correlation coefficient)??????????(Pearson correlation coefficient) ,???????????????????? ?????????,??????????????,???????????,??????????

    14. ????????? ??????????

    15. ????????? ??????????????, ??????????????????, ??????????? : ????????????????????????? ?????????????????????????, ????????,????????????????????????????????,?????????????????????????????????,??????????????????, ??????????, ????????????????????, ?????????, ??????????????????????? 0?“?????, ???????????” ?????, ?????????—????, ??????? (??????????(?????) )

    16. 14.1.2 ???????(?) ?????? ??µX,sX?????X????????; µY,sY?????Y????????; sXY?????X?Y??????

    17. 14.1.2 ???????(?1) ?X?Y???????????????

    18. 14.1.2 ???????(?2) ???????: ???????? –1 ? 1 ??? ??XY=1,??X?Y??????,???X???, Y????????;??,??? ??XY= –1 ,??X?Y??????,???X???, Y?????????;??,??? ??XY= 0 ,??X?Y????????,??????????????????(??????)???

    19. 14.1.3 ??????? ?????????????????(Bivariate normal distribution),???????? ,?????????,??????: ??

    20. ?14.2 ??14.1 ??????????????????,???Excel???????, ????: ???14.1???? ???????????????????? ? ??????$A$1:$B$10 ,????? ????rXY=0.425265 ?

    21. 14.1.3 ???????(?) ?14.2 ????XY?,X?Y????

    22. 14.1.4 ??????? ?XY=0??? ?? H0: ?XY = 0 H1: ?XY ? 0 ????? ??XY=0?(x,y)?????????,????? t* ?????? n-2 ? t ???

    23. ?14.3 ??14.2 ??14.1?,??a=0.05????,????????????????????????????? H0: ?XY = 0 H1: ?XY? 0 ?????: ???:

    24. ?14.3 ??14.2(?) ????: ???????: ?????H0,????????????????????????

    25. 14.1.4???????(?) ?XY = ?0??? ?? H0: ?XY = ?0 H1: ?XY ? ?0 ???????Fisher?? Zr

    26. 14.1.4 ???????(?1) ?XY = ?0??? ?n > 30?, Zr???????,? ,?? ??????Z?????,??

    27. ?14.4 ???????? ???????????????????,???????36?????,?????????0.68,??0.05??????,???????: H0:?XY = 0.75 H1:?XY ? 0.75 ??

    28. ?14.4 ????????(?) ???????? ? ,?????H0 ,??????????????????????????0.75 ?

    29. 14.2 ???????? 14.2.1 ????????????? 14.2.2 ???????

    30. 14.2 ????????(?) ????????(simple regression analysis) : ?????????(???)?????,???????????????? ???(scatter diagram) ???: ?????? X ???? Y ??,?????????????(????????????,? X ? Y ??????????????????????)?

    31. ??????? ??????????????????,????????????????????,??????,?????,??????????????,????????????????? ???????????,???????????,????????: ????????????????????? ?????????????????????? ????????????? ???????????????? ???????????????? (????????—???????????????)

    32. ????? ?????????????????, ??????????????? ?1,?????????,??????

    33. ?14.5 ???????? ABC????????????????(X)????(Y)????????????10???????????????14.3,???(?)?????????????????????????????

    34. ?14.5 ????????(?) ?14.3 10????????????(??:??)

    35. ?14.5 ????????(?1) ??14.3???????14.3,??14.3????,??????????????????,??????????????????????????????? ?14.3 ????????????

    36. 14.2.1 ????????????? ????????(simple regression model) : Y=? + ?X + ? ? X=xi????,?yi?X=xi?????,? ??ei?X=xi??????

    37. 14.2.1 ?????????????(?) ???? Y????,??????(?)????? ? X????,????????,????? ????????? ?~N(0, ?2)? Cov(?i, ?j)=0;?i?j?

    38. 14.2.2 ??????? ?????????(simple linear regression equation)????????(simple linear regression line) ??? X=xi????,?yi?X=xi?????,??

    39. 14.2.2 ???????(?) ????,E(Y)?????X??????Y????(???)? a??????X=0?,E(Y)??? ß??????X??????,E(Y)??????? ??,??????????X????,?????Y?????????,????????? ??????????,??????????????????????14.4???????

    40. 14.2.2 ???????(?1) ?14.4 ??????Y?????

    41. 14.3 ???????????? —????? ??a?b,????a?ß??????, ??Y????,??????????(estimated linear regression equation) : ?X=xi????,??????????:

    42. 14.3 ???????????? —?????(?) ?????(least square method) ? Q ???? ? ???????,???????????? Q ???????,???? a ? b ,??? ? ? ?????

    43. 14.3 ???????????? —?????(?1) ??????

    44. 14.3 ???????????? —?????(?2) ???????????: ??, ?X????, ?X?Y????????

    45. ????????? ?????????(Stigler) “?????????????????????????,???????????????????????”

    46. ?14.6 ??14.5 ???14.3?????????????????????????? ??14.3??????14.4?????a?b?

    47. ?14.6 ??14.5(?) ?14.4 ABC???????????????

    48. 14.4 ????????? ??????????????????????????????????????,?????????????(goodness of fit)? ??????????,???????(coefficient of determination)????????????????,???????????,????????????Y????????

    49. 14.4 ?????????(?) ?????????

    50. 14.4 ?????????(?1) ?????:

    51. 14.4 ?????????(?2) ???????:

    52. 14.4 ?????????(?3) ????(coefficient of determination; R2) R2 ????0?1??? R2 ??,?????????????????? ?????????????,?R2 ????????????????????,???Y???X????? ?

    53. 14.4 ?????????(?4) ?????????:

    54. 14.4 ?????????(?5) ???????,??????SST?SSE????,??????????,????????????????,?????????(adjusted coefficient of determination),??? ???,? ???? ??R2?,????????????,?????????,????????????

    55. ?14.7 ??14.6 ????14.6?????????????,???14.4??

    56. ?14.7 ??14.6(?) ????? ?ABC???????,????85.07%????????????????,??????????????????85.07%? ???????

    57. 14.5 ???????? 14.5.1 ? ? ? ?????? 14.5.2 ??????F??

    58. 14.5 ????????(?) ??a?ß????a?b?????Y???,?Y???????????e????s2 ,??????s2????? ???????e????s2 : SSE?????(mean square error) MSE?????????s2??????,? ,??

    59. 14.5.1 ? ? ??????? ??Y??????,??a?b???????????, ??

    60. 14.5.1 ? ? ???????(?) ?? ? ??? ??:H0: ? = 0 vs. H1: ? ? 0 ?????: ????: ? ?,??H0? ?: ????????30?,????z??,????????? ?????? ? ??????

    61. 14.5.1 ? ? ???????(?1) ? ?(1-?)%????:

    62. ?14.8 ??14.7 ???????0.05????,???????????????? ????????: H0:? = 0 vs. H1:? ? 0 ???????: ??

    63. ?14.8 ??14.7(?) ?? ,???? H0,?????????????????? ?ABC???????,ß?95%??????:

    64. 14.5.1 ? ? ???????(?2) ?? ? ??? ??:H0:? = 0 vs. H1:? ? 0 ?????: ????: ? ?,??H0? ?: ????????30?,????z??,?????????

    65. 14.5.1 ? ? ???????(?3) ? ?(1-?)%?????

    66. 14.5.2 ?????? F ?? ????????????? ??????? H0:???????????(? = 0) H1:??????????(? ? 0) ?????: ????: ,???H0?

    67. 14.5.2 ?????? F ??(?) ?14.5 ??????

    68. ?14.9 ??14.6 ??F??????????????????,???14.6????????,???????14.6 ?14.6 ABC???????? ????H0,???????????????????

    69. 14.6 ??????????????? ???????????,?????????,??????R2??,????????????????????,???????? ? ?,????????????,???????????????,? ??,???????????,? ???

    70. 14.6 ??????????? ????(?) X=x0??? ???? , ?(1-a)%???? ?:?????, tn-2,a/2?za/2???

    71. ?14.10 ??14.6 ???????????????25???,????????????95%???????? ???????? ??????25???,?????????99.07???

    72. ?14.10 ??14.6(?) ??????95%????? ??,??????25??,95%????????,???????????96.97???101.17?????

    73. 14.6 ??????????? ????(?1) X=x0??? ??

    74. 14.6??????????? ????(?2) ?(1-a)%???? ?:?????,tn-2,a/2?za/2???

    75. ?14.11 ??14.6 ?????25??????????????95%???????? ??????25???????????99.07???

    76. ?14.11 ??14.6(?) 95%????? ??????25??,95%??????,?????????92.19???105.95?????

    77. 14.6 ???????????????(? 3) ? ?? ?????? ?? ? ??? ,? ? ??,?????????? ??,???????? ??? X ?????,? ? ??,??????????

    78. 14.7 ???? ????????????? ????? ? ????????? ????? ? ??????? ????? ? ????? ??????????

    79. 14.7 ????(?) ????,??????????????????????: ???: ?????????????,?????????????? ???: ??????,???????????x??????,??????????,?????? ???: ??????,??????????????????????,??????????????????,???????????,????????

    80. 14.7 ????(?1) ????(residual analysis) ??????? X ??????????? Y ?????????????,??????????????? ??(residual) : ??????????????????????????,???e??,??i??????ei,??

    81. 14.7 ????(?2) ??????X???? ?14.6 ??????????X????

    82. 14.7 ????(?3) ?14.6 ??????????X????(?)

    83. 14.7 ????(?4) ?ABC??????X???????14.7 ?14.7 ABC??????X????

    84. 14.7 ????(?5) ??14.7?,?????,??????????????????,???????ABC???????????????(????Excel??)

    85. 14.7 ????(?6) ??????Y???? ???,????????X?????????? ???????? (normal probability plot) ????? ? ????????,???????????????,???????????? ??

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