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1、 1統計學統計學 II 期中考期中考 解答解答 1.(a)12222()()()/cov(,)()/()iiiiiixiiiXX YYX YXYnX YbSXXnXX=10.125 01106 10.125 825bYb X=?25 10.125iYX=+(b)ANOVA talbe S.S.d.f.M.S.F Regression 1640.412 1 1640.412 62.71 Error 261.588 10 26.159 Total 1902 11 2222(1)()()/1902TotalyiiiSSnSYYYYn=222cov(,)(1)261.588yxX YSSEnSS=19
2、02261.5881640.412TotalSSRSSSSE=1640.4121SSRMSR=26.15910SSEMSE=62.71MSRFMSE=(c)212226.159var()1.635(1)16()xiSMSEbnSXX=(d)01:0H=11:0H 檢定統計：11110.12507.9181.635bbTS=拒絕域：0.025,10|2.228Tt=Reject 0H 證據足以明廣告對銷售額無影響，即廣告費用與銷售額有線性關係 2 2.(a)1,2,121,1,1,2,22,1,2,2,()()()iiiiiiiiiinXXXXX XXX XX=X X 2154452528126
3、0676215445252812606761152812134113165281213411316103326318834860676131626966067613162696332112921960621960531=1,2,728()245684373iiiiYYX YXY=X 1()bY=X XX=21544525281260676728152812134113162456818834860676131626964373=29.8371.3450.271?1,2,29.837 1.3450.271iiiYXX=+(b)Y X1X2?Y e 60 2410 59.407 0.593 63
4、2712 62.900 0.100 70 3310 71.512-1.512 75 350 76.912-1.912 80 412 84.440-4.440 72 368 76.089-4.089 90 385 79.592 10.408 67 286 65.871 1.129 69 327 70.980-1.980 82 383 80.134 1.866 2()753.6TotaliSSYY=?2()159.741 iiSSEYY=3 2159.741110.788753.6TotalSSERSS=2/3.10.727/1TotalSSE nadj RSSn=(c)(此題用第一題之公式解，改
5、用矩陣解，亦可得到相同答案)111,121,1,1033272823.739()33211292245681.478iiiiiinXYbYXXX Y=X XX?1,23.739 1.478iiYX=+(d)2164.867110.781753.6TotalSSERSS=2/2.10.754/1TotalSSE nadj RSSn=(e)因為Model II 的2.adj R較高，所以選擇Model II (f)?1,2,29.837 1.3450.271iiiYXX=+情形 1：X1=30,X2=10 情形 2：X1=30,X2=0 所以平均體重相差 210b=2.71(公斤)-1-1-1va
6、r()var(var()var(bY=+=+X X)XX X)X XX X)X -1-12-1var(=X X)XX(X X)X X)2154452528126067620.608var()(52812134113161883486067613162696bMSE=-1X X)var(b2)=(20.608)(2696)/188348=0.295 22var(10)100var()bb=10000(0.295)=29.25 所以此估計的誤差為 29.25 4(g)殘差分析 (1)看殘差值的直方圖，圖型是否像常態分配 Histogram012345-5-2147101316ResidualFrequency (2)看殘差與?Y，檢查是否變為常 Residuals versus Predicted-10-50510155060708090PredictedResiduals (3)檢查殘差與X1是否有關 Residuals versus X1-10-5051015202530354045X1Residuals (4)看殘差之間彼此是否獨 Residuals versus Order-10-5051015024681012OrderResiduals