: ( .

2 27 ( ) 2 3 4 2 ( ) 59

Y n n U i ( ) & smith H 98 Draper N Curran PJ,bauer DJ & Willoughby Kam,Cindy &Robert 23 MT24 Jaccard,J & Rebert T23 Franzese 23 Aiken LS & West SG 99 " Multiple Regression Testing and interpreting Interaction Newbury Park sage Publications" 6

2 27 ( ) Y n n U i i Y Stata, Statistica, SPSS, Eviews 6

Stepwise Romove Interaction () 2 Y Y Y 2 2, 2 Y 2 i 2 (5 497) 28/29 62

2 27 2 ( i j j Y 2 3 2 U i 2 3 Y 2 Y 3 Y 2 2 Y Y 2 3 ( ) ( ) http //membersaolcom/imsap/mmrhtm http//wwwchassncsuedu/garson/pa/765/regresshtm 63 2 3

64 4 Y 2 2 3 5 Z=2 n (n +) Z n 4 U i Y 3 2 7 3 2 6 3 5 2 4 3 3 2 2 C ) G E ( S 4 http//wwwtuftsedu/~gdallal/reginterhtm 5

2 27 C G C E 2 C S 3 GE 4 C GS 5 C ES 6 C GES 7 C 65

6 Y 2872 24 3 2 2 3 4 2 3 2 4 3 4 2 3 2 4 3 4 2 3 4 2 3 4 http//wwwrufriceedu/~branton/interaction/faqintprhtm 6 66

2 27 Model Model Summary b Adjusted Std Error of R R Square R Square the Estimate 766 a 587 587 34988 a Predictors (Constant), 234, 3, 2, 3, 34, 4, 24,, 23, 23, 2, 24, 4, 34, 234 b Dependent Variable Y Model Regression Residual Total ANOVA b Sum of Squares df Mean Square F Sig 437E+2 5 29E+ 27252 a 37E+2 2873 6936254 743E+2 2878 a Predictors (Constant), 234, 3, 2, 3, 34, 4, 24,, 23, 23, 2, 24, 4, 34, 234 b Dependent Variable Y Coefficients a Model (Constant) 2 3 4 2 3 4 23 24 34 23 24 34 234 234 a Dependent Variable Y Unstandardized Coefficients Standardized Coefficients B Std Error Beta t Sig 2546368 5977 88 787957 75336 88 97 2467 2428 35 2 263 37276 4273 47 3254 33 435 355 2993 3 84553 23457 39 3954 8694 79 53 2636 8 57 78 222 9252 5279 47448 44 255 2 82 34 287 24 6 238 6 93 7723 747 78378 5 366 72 63 58 246 865 755 3 2776 2589 49 26 373 3329 269 23 293 687 Y=2546+7879 +246 2 372 3 +3 4 846 2 +869 3 + +5 4 52 2 3 +8 3 4 +7 2 3 76 2 4 4 2 3 4 + +27 2 3 4 67

3 Histogram Dependent Variable 2 Frequency 2 8 4 4 8 2 6 2 24 28 Std Dev = Mean = N = 2879 Regression Standardized Residual () Normal PP Plot of Regression Standardize Dependent Variable 75 Expected Cum Prob 5 25 25 5 75 Observed Cum Prob (2) 68

2 27 2 Partial Regression Plot Dependent Variable 2 3 4 6 5 4 3 2 (3) 2 Partial Regression Plot Dependent Variable 2 3 4 4 3 2 2 (4) 69

2 Partial Regression Plot Dependent Variable 2 3 4 4 2 8 6 4 2 2 4 (5) 2 Partial Regression Plot Dependent Variable 2 3 4 2 (6) 7

2 27 2 Partial Regression Plot Dependent Variable 2 3 4 2 3 2 (7) 2 Partial Regression Plot Dependent Variable 2 3 4 2 2 4 6 8 2 4 3 (8) 7

2 Partial Regression Plot Dependent Variable 2 3 4 4 2 2 4 6 4 (9) Partial Regression Plot Dependent Variable 2 2 3 4 4 2 2 4 6 8 23 () 72

2 27 2 Partial Regression Plot Dependent Variable 2 3 4 2 3 24 () 2 Partial Regression Plot Dependent Variable 2 3 4 2 2 3 4 34 (2) 73

Partial Regression Plot Dependent Variable 2 2 3 4 8 6 4 2 2 23 (3) 2 Partial Regression Plot Dependent Variable 2 3 4 2 8 6 4 2 2 4 24 (4) 74

2 27 2 Partial Regression Plot Dependent Variable 2 3 4 2 34 (5) 2 Partial Regression Plot Dependent Variable 2 3 4 6 4 2 2 4 234 (6) 75

2 Partial Regression Plot Dependent Variable 2 3 4 2 2 3 234 (7) (6) (2) Remove Model Summary(e) Model R R Square Adjusted R Square Std Error of the Estimate 766(a) 587 587 34988 2 766(b) 587 587 3434 3 766(c) 587 587 3497 4 766(d) 587 587 3482 76

2 27 ANOVA(e) Model Sum of Squares df Mean Square F Sig Regression 436542986927778 5 292865379585 27252 (a) Residual 369384737964827 2873 693625432 Total 7434845448926 2878 2 Regression 4365295625856463 4 386834839 2958 (b) Residual 36958993642 2874 693697464 Total 7434845448926 2878 3 Regression 4365257829452759 3 335789638458 3436 (c) Residual 36955675439846 2875 6934565945 Total 7434845448926 2878 4 Regression 43652942463555 2 363768285384463 3486 (d) Residual 36959522795 2876 693278648 Model Total 7434845448926 2878 Coefficients(a) Standardized Unstandardized Coefficients Coefficients t Sig B Std Error Beta (Constant) 2546368 5977 88 787957 75336 88 97 2 2467 2428 35 2 263 3 37276 4273 47 3254 4 33 435 355 2993 3 2 84553 23457 39 3954 3 8694 79 53 2636 8 4 57 78 222 9252 23 5279 47448 44 255 2 24 82 34 287 24 6 34 238 6 93 7723 23 747 78378 5 366 72 24 63 58 246 865 34 755 3 2776 2589 234 49 26 373 3329 234 269 23 293 687 77

2 (Constant) 36522 67233 2242 69777 5237 78 96 3 725664 279737 59 669 4 88 423 323 288 5 2 62673 27227 8 4926 3 2342 6683 6 393 4 57 78 237 9522 23 8429 36968 7 595 552 24 949 32 332 2967 3 34 277 56 932 869 23 48 5887 23 828 48 24 647 56 279 53 34 759 3 2788 2532 234 464 9 44 3895 234 274 22 32 223 3 (Constant) 35937 6774 2233 692678 52335 78 2 3 8442 239653 62 7559 4 86 423 323 282 5 2 62587 2727 8 499 3 23393 57266 66 484 4 59 78 239 9555 24 954 32 334 2984 3 34 287 56 939 8273 23 292 48394 4 599 549 24 649 56 283 595 34 76 3 2796 256 234 474 8 422 4 234 277 22 332 2526 4 (Constant) 342455 6567 295 6482 32957 73 2396 3 7592 26764 6 874 4 235 45 336 2976 3 78

2 27 2 55328 38843 96 4243 3 252762 47844 72 5283 4 56 78 235 9555 24 927 36 324 2928 3 34 268 52 925 839 24 65 56 285 69 34 76 3 2794 2567 234 464 7 43 3965 234 277 22 335 258 a Dependent Variable Y Y=34246+6483723+245332+25273+ +54+924+33483465245234+ +28234 Stepwise Model Summary(n) Model R R Square Adjusted R Square Std Error of the Estimate 682(a) 465 465 76468 2 72(b) 52 52 48588 3 75(c) 564 564 6258 4 757(d) 573 573 597 5 76(e) 578 578 453453 6 763(f) 58 58 449 7 764(g) 584 584 379692 8 764(h) 584 584 37472 9 765(i) 585 584 372626 766(j) 586 586 35395 766(k) 587 586 347548 2 766(l) 587 587 345488 3 766(m) 587 587 34977 79

ANOVA(n) Model Sum of Squares df Mean Square F Sig Regression 3462983926994 3462983926994 25425 (a) Residual 397465469656 2877 384625 Total 7434845448926 2878 2 Regression 38656739275986 2 932836963759593 555899 (b) Residual 356946737349 2876 242992 Total 7434845448926 2878 3 Regression 49267584368623 3 3975579478954 2377879 (c) Residual 32424296523982 2875 29764274 Total 7434845448926 2878 4 Regression 426323768865983 4 658942264796 9649349 (d) Residual 37576856233422 2874 45424386 Total 7434845448926 2878 5 Regression 429724934768 5 8594429868354 786497 (e) Residual 33764585837 2873 9274685747 Total 7434845448926 2878 6 Regression 4323562232684 6 725937543347 664895 (f) Residual 37583263252 2872 837839923 Total 7434845448926 2878 7 Regression 434548793577535 7 6222256225362 5756755 (g) Residual 39326575357 287 77386 Total 7434845448926 2878 8 Regression 434462976958956 8 543787469869 545585 (h) Residual 3984827933649 287 763444934 Total 7434845448926 2878 9 Regression 434597388477777 9 48288597879753 448848 (i) Residual 3888473644828 2879 75937332 Total 7434845448926 2878 Regression 43587269688456 4358726968845 46788 (j) Residual 376848899 2878 753879 Total 7434845448926 2878 8

2 27 Regression 436597745753 3964647973432 37279 (k) Residual 37378567846852 2877 77744447 Total 7434845448926 2878 2 Regression 43624367298268 2 36353639349855 339662 (l) Residual 37237782299997 2876 7296662 Total 7434845448926 2878 3 Regression 436522229623873 3 335786334767 3474 (m) Residual 369592248768732 2875 693583824 Total 7434845448926 2878 n Dependent Variable Y Model Unstandardized Coefficients Coefficients(a) B Std Error Beta Standardized Coefficients t Sig (Constant) 534746 78299 96 4 257 6 682 585 2 (Constant) 44584 75842 9539 4 4285 35 66 23939 34 46 3 537 576 3 (Constant) 7254476 529 47724 4 4744 34 29 39365 34 94 3 7 746 239699 3976 225 5386 4 (Constant) 8425397 57323 53555 4 4369 37 89 8736 34 296 5 89 663 83928 458 9 43459 4 349 4 492 25276 5 (Constant) 855836 56643 54588 4 4798 44 36 95 34 33 5 5 649 768596 4335 86 42787 4 45 4 585 2952 24 46 26 6 7632 6 (Constant) 8638647 563 5534 4 466 45 256 88 34 439 9 63 46337 7249 4278 8 473 4 75 26 59 2896 8

24 822 92 637 9829 234 574 37 5 5443 7 (Constant) 64344 28266 48764 4 445 48 99 9822 34 45 9 659 47562 7277 456 8 4834 4 784 26 4 38 24 22 93 73 2698 234 77 39 639 856 23 66346 5637 57 3 8 (Constant) 74838 294 497 4 5447 2 482 277 34 4 2 55 33332 797 424 8 4478 4 676 33 952 2546 24 242 8 84 237 234 89 5 793 7666 23 687935 582 6 3537 34 422 79 38 535 9 (Constant) 67249 2249 485 4 5665 2 542 273 34 428 3 573 327 7922 424 8 4548 4 668 33 94 225 24 2564 26 896 2273 234 853 5 76 6597 23 666778 56 58 333 34 395 79 288 4975 234 9 5 9 3534 (Constant) 8894 22496 49384 4 864 47 57 4583 34 7 29 26 24396 677396 424 76 4673 4 45 76 994 863 24 588 35 25 863 62 234 294 7 262 25 2 23 7934 527 62 388 34 985 49 79 66 234 25 22 28 437 24 68 56 23 94 (Constant) 997693 29296 346 4 849 46 53 4549 82

2 27 34 76 29 2633 2459 2856 8397 22 2429 4 47 76 997 8645 24 743 37 26 2345 9 234 36 8 32 36 2 23 439 7845 37 5487 34 2 49 73 674 234 263 22 265 94 24 628 56 242 232 2 27726 58645 48 4728 2 (Constant) 9748 474 26956 4 63 42 439 397 34 73 29 268 24845 2768 93752 229 2364 4 438 76 226 8866 24 84 38 285 2564 234 44 9 369 3487 23 52552 6 3 373 7 34 2 53 87 7322 234 27 22 299 28 24 634 56 254 338 2 432354 73297 75 5899 3 659389 872 23 3526 3 (Constant) 342584 62695 247 4 243 48 338 2974 3 34 76 3 279 25374 64945 39983 73 722 4 55 78 234 956 24 92 38 322 2896 4 234 46 9 4 386 23 8699 42 2 64 87 34 263 55 922 827 234 277 22 333 2479 24 65 56 285 65 2 542442 76374 94 72 3 7223 279684 59 654 3 259 496 7 54 a Dependent Variable Y Y=3426+649 722 3 +2 4 5424 2 +5 4 52 2 3 +3 3 4 65 2 4 46 2 3 4 +28 2 3 4 83

F t (VIF) Pvalue 7 ( 8 ) 7 Understanding Interaction Models Improving Empirical Analyses Thomas Brambor(New York University, Department of Politics,) William Roberts Clark (University of Michigan, Center for Political Studies), Matt Golder (Florida State University, Department of Political Science,) 8 27 7 84

2 27 9 Pvalue t F (VIF) (52 32) 29 9 9 85

2 3 4 2 ( ) 5 Y=2546+7879 +246 2 372 3 +3 4 846 2 +869 3 + +5 4 52 2 3 +8 3 4 +7 2 3 76 2 4 4 2 3 4 + +27 2 3 4 Y=34246+648 372 3 +245533 2 +2527 3 +5 4 + +9 2 4 +3 3 4 8 3 4 65 2 4 5 2 3 4 +28 2 3 4 Y=3426+649 722 3 +2+5424 2 +5 4 52 2 3 + +3 3 4 65 2 4 46 2 3 4 +28 2 3 4 2 Stepwise 3 86

2 27 28 2 27 7 3 998 999 2 2 29/28 4 REFERENCES Aiken, L S, and S G West (99) Multiple regression Testing and interpreting interactions Newbury Park Sage Publications 2 Cohen, J (978) Partialed products are interactions; partialed vectors are curve components Psychological Bulletin, 85, 858866 3 Darlington, R B (99) Regression and linear models New York McGrawHill 4 Donald F Burrill Modeling and Interpreting Interactions in Multiple RegressionThe Ontario Institute for Studies in Education Toronto, Ontario Canada 5 Goldberg, A E, & Sayer, A (26) Lesbian couples' relationship quality across the transition to parenthood Journal of Marriage and Family, 68, 87 6 Kennedy, J K, Bolger, N, & Strout, P E (22) Witnessing interparental psychological aggression in childhood Implications for daily conflict in adult intimate relationships Journal of Personality, 7, 5277 7 Paul D Allison Testing for Interaction in Multiple Regression The American Journal of Sociology, Vol 83, No (Jul, 977), pp 4453 8 Story, L B, & Repetti, R (26) Daily occupational stressors and marital behavior Journal of Family Psychology, 2, 697 9 William Roberts Clark (University of Michigan, Center for Political Studies), Matt Golder (Florida State University, Department of Political Science,) Understanding Interaction Models Improving Empirical Analyses Thomas Brambor(New York University, Department of Politics,),(27) 87

http//membersaolcom/imsap/mmrhtm 2http//wwwchassncsuedu/garson/pa/765/regresshtm 3http//wwwtuftsedu/~gdallal/reginterhtm 4http//wwwtuftsedu/~gdallal/reginterhtm 5http//wwwrufriceedu/~branton/interaction/faqintprhtm 29/2/3 88