城市規(guī)劃系統(tǒng)工程學課程習題.doc

第二章習題：證明題1：設（X1，X2，Xn）為來自總體X的樣本，EX=a，DX=2則（1）=a，=2/n （2）ES2=2證明題2： a是以外的任何數值，即離均差平方和為最小。第三章習題：1.證明題：對于平均中心（中項中心）的離散程度 - 標準距離 - 區(qū)內標準距離 - 小區(qū)間標準距離2.求 到最短路徑，并寫出步驟271553515732 第四章習題：1 例如在某地理區(qū)域取得個169個某要素的地理數據，算得平均數為，標準差 ；又在相鄰的另一地理區(qū)域，測得99個數據，算得平均數，標準差。問兩個地理區(qū)域可否看成同一類型（同一母體）2如有上海1873-1972年一百年降水資料（見下表），問是否滿足正態(tài)分布？01234567891870947.81806.31588.1769.81008.91206.81271.418801101.91340.2133110851184.41113.41204.91170.7975.41462.31890947.114167091147.59351016.31031.61105.7849.91233.419001008.61063.81004.91086.21022.51330.91439.41236.51088.11288.719101115.81217.51320.71078.11203.414801269.91049.21318.41191.819201015.51507.11159.61021.3986.1794.71131.51170.61161.7791.219301143.81602951.41002.5859.4870.69121025.21264.21196.519401140.71659.3942.71123.3910.214051208.71305.51167.21225.919501402.51256.11285.9984.811951062.31287.3147710171217.719601191.111431018.81243.7909.31030.31124.4811.4820.91184.119701107.5911.4901.7 3某市交通管理部門將一天分為三個時段，其中4時到12時為商務，12時到20時為下午，20時到次日4時為夜間，對某一路段的交通量進行了觀測，集體數據見下表觀測值時段上午下午夜間交通流量86208930350077508750420078208430324081507940381081307980289010040954047209900108004870要求：（1）試采用單因素方差分析方法判斷，在顯著性水平下，上午、下午和夜間這三個交通時段里的交通流量是否存在顯著性差異。（2）試采用T統(tǒng)計量的假設檢驗方法對上午、下午和夜間這三個水平之間的差異性進行多種比較。第五章習題：1 以一元線性回歸為例，證明 (相關系數)2 某城市人口密度（萬人/），與市中心距離以公里（）計，抽樣調查如下： No102.8854222.1493351.3910470.9737590.7043求非線性回歸方程（用指數模型）。3 證明題 多元線性回歸 （） 4 城市用水量y和工業(yè)產值（）、工業(yè)門類結構（輕工比例）（）、城市人口規(guī)模（）及居民用水標準（）四個主要因素有關，試建立多元回歸方程。年份（億元）（%）總用水量y（萬噸/年）19553.141695.731.647.8119.119608.465764.739.2028.4552.9119658.161570.843.3119.0915.9197015.339655.040.0033.21426.48197527.099451.344.0050.22391.01197733.003752.945.0068.43389.98197942.241053.445.0089.74848.30198049.253757.347.00105.05912.535以收集到的某地18口鉆井資料（Z2層 的厚度變化如下表）為例，對Z2層厚度變化進行趨勢面分析（(求三次趨勢面數學函數模型)）測點編號坐 標厚 度（米）測點編號坐 標厚 度（米）XYXY14.212.85231214.593.2225963.931.7248.5224.593.2325975.041.55196234.12.84261.583.851.11211284.682.7527294.533.22248.5294.72.75276.5124.582.75244303.771.32253.5164.72.17590323.913.48259.5184.892.72280.4374.573.22225.5204.563.19241442.482.8613第六章習題：1. 假定某市某個時期對某種消費品的銷售量為y，居民可支配收入為，該類消費品的價格指數為，社會保有量為，其他消費品的價格指數，試研究該市對這種消費品的需求函數。原始數據如下：n居民可支配收入該類消費品的價格指數社會保有量其他消費品的價格指數銷售量y182.992.017.194.08.4288.993.021.396.09.6399.996.025.197.010.44105.394.029.097.011.45117.7100.034.0100.012.26131.0101.040.0101.014.27148.2105.044.0104.015.88161.8112.049.0109.017.99174.2112.051.0111.019.310184.7112.053.0111.020.8用逐步回歸方法求最優(yōu)回歸方程。第七章習題：1. 已知一批樣本數據如下： 指標樣本編號 x1x2x3x4x5類別114.188.7160.785.87.11237.8116.8159.9112.811.71338.6134.385.6147.212.62472.9246.775.2284.613.8350.459.8143.659.910.916129.7225.267.8235.213.63773.598.269.7119.711.12837.169.2104.5128.413.92959.287.5118.5899.711031.553.9114.280.61011143.485.7155.880.310.51129.590.4143.7118.6151136.8194.9108.2144.913.611414.3107.3140105.36.911546.5129.1154.191.311.911643143.183.9157.41321771.2280.582.5317.413.93180.769.3145.669.511.3119123.9297.364.6307.213.732085.4115.439.4144.711.112138.477.394.6143.213.922279.696.885.4999.622333.474.7129.5103.49.912448.195.9155.39210.51257.7116.3158.2148.115.11268.9225.3104.2195.513.812734.8150.7165124.611.912844.4147.288.3158.712.722974.2232.794.1154.913.53300.180.9148.881.311131119.620870.9217.813.833294130.249.2176.21123332.983.6115.3135.713.823465.588.1126.9102.59.713531.359.3105.182.91013652.393.3173.791.2101377.298.2154.3120.7151385.3245.8100.4200.213.713925.3173.660.398.513.50（待判樣品）4021.9147.353.99813.60（待判樣品）4128153.263.1109.313.60 （待判樣品）要求：（1）.用聚類分析方法對樣本進行分類（2）.使用逐步判別分析,求fisher總則判別函數,并對樣本39，40，41分類;（3）.求Bayes總則判別函數，并對樣本39，40，41分類。第八章習題：1證明主成分載荷 （i=1,2,.,p;k=1,2,m）是主成分與變量之間的相關系數2以兩個變量主成分為例證明主分量 和 是無關的（正交）。3.證明p個主分量的總方差與原p個變量的總方差相等4. 對下表數據進行如下操作（1）.求前三個主成份得分系數距陣（2）.寫出各變量的因子表達式X1X2X3X4X5X6X7X8X9272.5104.626.90.3764856944591746.9281.1112.3281.0311465839465.115.169.7282.2113.528.12.313085894490.515.273.1285.6124.230.42.4712196008492.714.758.3309.3135.632.95.4610536096509.716.463.6319.1138.232.56.8610806188515.616.152333180.543.417.163245552503.515.840.5327.9173.942.418.282145487473.215.564.1311.5156.740.324.553835672473.815.259.7288.5139.838.835.56754584950216.169.4283.9137.838.844.6512566042523.916.861.927812836.867.9715246227552.415.855.7260.6120.437119.5416986413574.816.328.3270.9133.539.4105.2517286627587.41562259.1126.739.158.7215846875600.114.285.6258.112639.198.5316297115605.216.474.6262.5130.939.9123.316107356617.513.649.4269.3139.641.5168.415397567641.716.333.6290.3166.445.9168.151898777064115.471.6297.7173.646.7208.381974800263317.183295.7173.749.9205.8118958205625.115.862.7291.117250.2231.3818078402615.216.138.5306185.651.6243.9617548504601.913.842.1310.9187.254.2365.2818318566582.315.481336.120454.6479.2321558575594.815.938.4350.5228.558.7542.862736859462615.451.5321.3217.460.95703100861562715.239.2299.1203.7805803200867062713.553.95某地區(qū)35個城市2004年的7項經濟統(tǒng)計指標數據見下表。（1）試用最短距離聚類法對45個城市綜合實力進行系統(tǒng)聚類分析，并畫出聚類譜系圖；（2）試用主成分分析法對45個城市7項經濟指標進行主成分分析，并分析其綜合實力；（3）以第一、二、三主成分為變量，進行聚類分析，結果又怎樣呢？城市編號總人口(單位：104人)非農業(yè)人口比例(單位:%)農業(yè)總產值(單位：108元)工業(yè)總產值(單位：108元)地方財政預算內收入(單位：108元)城鄉(xiāng)居民年底儲蓄余額(單位：108元)在崗職工工資總額(單位：108元)11249.90 0.60 184.34 1999.97 279.09 2680.66 577.33 2910.17 0.58 150.11 2264.55 112.81 1130.19 225.43 3875.40 0.23 291.87 688.58 35.23 709.59 75.89 4299.92 0.66 23.60 273.78 20.33 394.31 65.40 5207.78 0.44 36.53 81.65 10.58 139.66 30.93 6677.08 0.63 129.54 582.67 56.79 901.70 115.28 7545.31 0.49 187.97 842.64 70.92 755.68 96.59 8691.23 0.41 185.32 596.63 35.71 480.37 88.44 9927.09 0.46 266.39 418.61 48.14 645.00 130.92 101313.12 0.74 206.90 5452.91 431.85 2597.12 560.54 11537.44 0.53 98.92 1307.27 66.43 568.05 135.79 12616.05 0.36 141.47 1200.08 44.96 742.60 118.09 13538.41 0.25 142.82 1062.29 50.17 524.64 82.40 14429.95 0.32 62.88 251.41 23.36 162.29 36.96 15583.13 0.27 215.23 655.54 46.75 503.02 68.06 16128.99 0.49 33.34 575.11 41.88 210.83 65.75 17424.20 0.40 68.83 230.59 16.77 264.05 47.96 18557.63 0.41 148.63 628.59 46.07 412.70 75.67 19702.97 0.37 238.23 1149.20 65.84 497.80 96.17 20615.36 0.34 67.74 528.76 38.73 513.53 69.68 21740.20 0.59 121.13 750.61 60.47 5