多变量分析考试试卷

1、多变量分析考題多变量分析考題 2014-1-16 100 位學生對 6 個問項評量，第 15 題皆以此資料檔做分析 61 xx Means and Standard Deviations (lattin-exer-5-4) variable MeanStd.Dev. x1 x2 x3 x4 x5 x6 0.184286 1.387459 0.202391 1.392293 0.142090 1.528200 0.053702 1.540235 -0.064150 1.539805 0.114520 1.491904 Correlations (lattin-exer-5-4) variable

2、 x1 x2 x3 x4 x5 x6 x1 x2 x3 x4 x5 x6 1.000 0.849 0.462 0.416 0.409 0.455 0.849 1.000 0.442 0.439 0.360 0.334 0.462 0.442 1.000 0.909 0.499 0.478 0.416 0.439 0.909 1.000 0.501 0.459 0.409 0.360 0.499 0.501 1.000 0.862 0.455 0.334 0.478 0.459 0.862 1.000 Factor Loadings (Unrotated) (lattin-exer-5-4) E

3、xtraction: Principal components (Marked loadings are .700000) Variable Factor 1 Factor 2 Factor 3 x1 x2 x3 x4 x5 x6 Expl.Var Prp.Totl -0.760073 -0.5537580.206876 -0.723208 -0.6275550.113820 -0.8221800.127733 -0.509738 -0.8079660.147651 -0.530870 -0.7796400.4292500.367067 -0.7693940.4104190.418883 3.

4、6293361.0912890.907610 0.6048890.1818820.151268 Factor Loadings (Varimax normalized) (lattin-exer-5-4) Extraction: Principal components (Marked loadings are .700000) Variable Factor 1 Factor 2 Factor 3 x1 x2 x3 x4 x5 x6 Expl.Var Prp.Totl 0.244000 0.911829 0.190237 0.126269 0.928733 0.226543 0.250025

5、 0.234622 0.913547 0.240833 0.205907 0.925222 0.909511 0.174184 0.263213 0.923116 0.195627 0.213217 1.875345 1.860032 1.892858 0.312557 0.310005 0.315476 Factor Loadings (Varimax normalized) (lattin-exer-5-4) Extraction: Principal components (Marked loadings are .700000) Variable Factor 1 Factor 2 x

6、1 x2 x3 x4 x5 x6 Expl.Var Prp.Totl 0.269230 0.901041 0.195191 0.937420 0.731507 0.396475 0.732266 0.372018 0.880330 0.130817 0.860770 0.139592 2.697805 2.022820 0.449634 0.337137 Chi-Square Tests with Successive Roots Removed (lattin-exer-5-4) Root Removed Canonicl R Canonicl R-sqr. Chi-sqr.dfp 0 1

7、0.534498 0.285689 42.323638 0.000001 0.318188 0.101244 10.193973 0.016999 Factor Structure, left set (lattin-exer-5-4) Root Variable Root 1Root 2 x1 x2 -0.998922 0.046420 -0.823896 0.566742 Variance Extracted (Proportions), left set (lattin-exer-5-4) Root Factor Variance extractd Reddncy. Root 1 Roo

8、t 2 0.8383250.239500 0.1616750.016369 Factor Structure, right set (lattin-exer-5-4) Root Variable Root 1Root 2 x3 x4 x5 x6 -0.8550290.362155 -0.7632410.571675 -0.7614820.138680 -0.858431 -0.244362 Variance Extracted (Proportions), right set (lattin-exer-5-4) Root Variable Variance extractd Reddncy.

9、Root 1 Root 2 0.6575930.187867 0.1342280.013590 Canonical Weights, left set (lattin-exer-5-4) Variable Root 1Root 2 x1 x2 -1.07361 -1.56075 0.087941.89231 Canonical Weights, right set (lattin-exer-5-4) Variable Root 1Root 2 x3 x4 x5 x6 -0.715801 -0.66171 0.1434141.30315 0.1002841.04824 -0.668422 -1.

10、42941 Summary for scale: Mean=.632839 Std.Dv.=6.91113 Valid N:100 (lattin-exer-5-4) Cronbach alpha: .869171 Standardized alpha: .868928 Average inter-item corr.: .570634 variable Mean if deleted Var. if deleted StDv. if deleted Itm-Totl Correl. Alpha if deleted x1 x2 x3 x4 x5 x6 0.448553 34.84056 5.

11、902589 0.646727 0.850661 0.430448 35.48915 5.957277 0.598464 0.858428 0.490750 32.45480 5.696911 0.722624 0.836953 0.579137 32.63802 5.712970 0.702411 0.840672 0.696989 33.07959 5.751486 0.672920 0.846086 0.518319 33.67872 5.803337 0.661891 0.847935 Analysis of Variance (lattin-exer-5-4) Effect Sums

12、 of Squares dfMean Square F Between Subjects Within Subjects Between Items Residual Total 788.10299 7.960628 520.380 500 1.040759 4.8485 0.969590 0.930975 515.532 495 1.041478 1308.482 599 1.主成份分析(利用 R 做主成份分析) (1) 對此組資料如要解釋變異數比例超過 80%，需選取多少個主成份？ 為什麼？ (2) 寫出第一主成份的權重； 1 x (3) 其中為第一主成份；r y x(,)? 11 1 y

13、 (4) 第一主成份共解釋多少變異數比例？ 1 y 61 xx (5) 第一、二主成份共解釋多少變異數比例？ 1 y 61 xx (6) 以解釋多少變異 ？ (12%)( 3 1 321 XXX 61 xx 2.因素分析：以主成份法選取 3 個因素，再做 VARIMAX normalized 旋 轉 (1)每個因素各有多少個變數(問項)？ (2) 3 個因素共解釋變異多少百分比？ 61 xx (3)因素一與 x1相關係數是多少？ (4)因素二的變異數=? (5)x1共通性=？ (6)因素一與因素二相關係數是多少？ (12%) 3 典型相關分析 將 8 個變數分成組=，組=做典型相關分析，x)(

14、 41 xxy),( 65 xx (1)對此組資料最多可取多少組典型變量？ (2)您會選取多少組典型變量？為什麼？ (3)典型相關=?),( * 1 * 1 yxr (4) =？),( * 11 yxr (5) y 組第一典型變量解釋 y 組的變異數比例為多少？y1 (6) ？ (12%) 2 |xy R 4.信度分析 (1)求6 個問項未標準化的 Cronbach 值是多少？ 61 xx (2)若將第 3 題()去除，試問剩下 5 題之未標準化 Cronbach 值=？ 3 x (3)檢定受測者間(即學生間)的平均數是否有顯著差異？F 值=？ (4) 求3 個問項標準化的 Cronbach

15、值是多少？ (12%) 31 xx 5. SEM 路徑圖如下 1.79 高中數理 X1 .11 d1 1.00 1 X2 .45 d2 .91 1 高中語文 X3 .11 d3 X4 .31 d4 1.00 1 .96 1 大學數理 x5 .31 e1 x6 .32 e2 1.00 1 .96 1 1.32 z2 1 1.67 z1 1 .40 Unstandardized estimates 卡方值=13.797 P值=.032 GFI=.955 AGFI=.842 RMSEA=.115 .54 .29 高中數理 .94 X1 d1 .97 .77 X2 d2 .88 .24 高中語文 .9

16、5 X3 d3 .87 X4 d4 .98 .93 .35大學數理 .87 x5 e1 .86 x6 e2 .93 .93 z2 z1 .41 Standardized estimates 卡方值=13.797 P值=.032 GFI=.955 AGFI=.842 RMSEA=.115 .49 .27 RegressionRegression Weights:Weights: EstimateS.E.C.R.PLabel 高中語文-高中數理 .54.114.81* 大學數理-高中語文 .40.103.85* 大學數理-高中數理 .29.112.49.01 X1-高中數理1.00 X2-高中數理

17、.91.108.80* X3-高中語文1.00 X4-高中語文.96.07 13.03* x5-大學數理1.00 x6-大學數理.96.09 10.26* 對此模式的適合度做評估； (1) 對此模式的適合度做評估； (2) 此模式的自由度=？ (3) 此模式是否有不合理的參數估計？ (4) 大學數理的結構信度 C.R.=？ (5) 大學數理萃取變異數 V.E.=？ (6) 大學數理的 2 R (7) 高中語文的 2 R (8) 高中數理到大學數理直接效用 (9) 高中數理到大學數理間接效用與總效用 (10)獨立模式的卡方值=？ (11)獨立模式的自由度=？ (12)檢定高中數理到大學數理路徑係

18、數是否為 0 的 t 值=？(25%) 第 6、7 題皆以此資料檔做分析 x1x2x3A CASE_NO CLUSTER DISTANCE C_1 56.12673134.26 C_2 66.23613232.78 C_3 67.44573334.54 C_4 53.84483411.86 C_5 464503516.4 C_6 70.65403619.02 C_7 58.45453711.52 C_8 54.95463811.12 C_9 58.36503912.09 C_10 46.263631023.14 C_11 67.174931116.27 C_12 5175131214.14 C

19、_13 44.1270213311.07 C_14 48.443021423.39 C_15 43.743021521.27 C_16 5054221614.75 C_17 45.454021724.94 C_18 39.852621823.8 C_19 47.763521923.38 C_20 42.263022021.28 C_21 39.663222122 C_22 52.874522212.67 C_23 4573522322.5 C_24 40.583112422.29 C_25 71.526912537.05 C_26 64.525612633.88 C_27 59.7260127

20、31.58 C_28 35.422012828.25 C_29 62.635612933.53 C_30 57.434613011.44 C_31 46.832513124.67 C_32 4134313226.65 C_33 58.845113312.76 C_34 40.442813422.69 C_35 46.753513522.86 C_36 37.653313623.14 . Classification Functions; grouping: a (lattin-exer-12-14) Variable G_1:0 p=.33333 G_2:1 p=.33333 G_3:2 p=

21、.33333 x1 x2 x3 Constant 0.61400.53150.6763 3.01113.74443.9084 0.18750.23890.2639 -26.0690-27.3547-36.7541 Analysis of Variance (lattin-exer-12-14) Variable Between SS dfWithin SS dfFsignif. p x1 x2 x3 2209.5571 1345.203 34 55.84657 0.000000 7.084193.889 342.56522 0.118489 4000.0341 1928.854 34 70.5

22、0877 0.000000 Analysis of Variance (lattin-exer-12-14) Variable Between SS dfWithin SS dfFsignif. p x1 x2 x3 2296.1022 1258.658 33 30.10006 0.000000 40.368260.604 33 10.99055 0.000220 5063.5352865.354 33 96.54812 0.000000 Classification Matrix (lattin12-14) Rows: Observed classifications Columns: Pr

23、edicted classifications Group Percent Correct G_1:0 p=.33333 G_2:1 p=.33333 G_3:2 p=.33333 G_1:0 G_2:1 G_3:2 Total 53.84615733 72.72727281 66.66666228 63.88889111312 Tree Diagram for 36 Cases Wards method Euclidean distances C_28 C_36 C_24 C_21 C_34 C_18 C_20 C_15 C_31 C_14 C_32 C_17 C_16 C_23 C_35 C_19 C_10 C_12 C_5 C_33 C_9 C_30 C_7 C_22 C_8 C_4 C_11 C_6 C_25 C_27 C_29 C_26