城市规划系统工程学课程习题.doc

第二章习题：证明题1：设（X1，X2，Xn）为来自总体X的样本，EX=a，DX=2则（1）=a，=2/n （2）ES2=2证明题2： a是以外的任何数值，即离均差平方和为最小。第三章习题：1.证明题：对于平均中心（中项中心）的离散程度 - 标准距离 - 区内标准距离 - 小区间标准距离2.求 到最短路径，并写出步骤271553515732 第四章习题：1 例如在某地理区域取得个169个某要素的地理数据，算得平均数为，标准差 ；又在相邻的另一地理区域，测得99个数据，算得平均数，标准差。问两个地理区域可否看成同一类型（同一母体）2如有上海1873-1972年一百年降水资料（见下表），问是否满足正态分布？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某市交通管理部门将一天分为三个时段，其中4时到12时为商务，12时到20时为下午，20时到次日4时为夜间，对某一路段的交通量进行了观测，集体数据见下表观测值时段上午下午夜间交通流量86208930350077508750420078208430324081507940381081307980289010040954047209900108004870要求：（1）试采用单因素方差分析方法判断，在显著性水平下，上午、下午和夜间这三个交通时段里的交通流量是否存在显著性差异。（2）试采用T统计量的假设检验方法对上午、下午和夜间这三个水平之间的差异性进行多种比较。第五章习题：1 以一元线性回归为例，证明 (相关系数)2 某城市人口密度（万人/），与市中心距离以公里（）计，抽样调查如下： No102.8854222.1493351.3910470.9737590.7043求非线性回归方程（用指数模型）。3 证明题 多元线性回归 （） 4 城市用水量y和工业产值（）、工业门类结构（轻工比例）（）、城市人口规模（）及居民用水标准（）四个主要因素有关，试建立多元回归方程。年份（亿元）（%）总用水量y（万吨/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口钻井资料（Z2层 的厚度变化如下表）为例，对Z2层厚度变化进行趋势面分析（(求三次趋势面数学函数模型)）测点编号坐 标厚 度（米）测点编号坐 标厚 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第六章习题：1. 假定某市某个时期对某种消费品的销售量为y，居民可支配收入为，该类消费品的价格指数为，社会保有量为，其他消费品的价格指数，试研究该市对这种消费品的需求函数。原始数据如下：n居民可支配收入该类消费品的价格指数社会保有量其他消费品的价格指数销售量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用逐步回归方法求最优回归方程。第七章习题：1. 已知一批样本数据如下： 指标样本编号 x1x2x3x4x5类别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（待判样品）4021.9147.353.99813.60（待判样品）4128153.263.1109.313.60 （待判样品）要求：（1）.用聚类分析方法对样本进行分类（2）.使用逐步判别分析,求fisher总则判别函数,并对样本39，40，41分类;（3）.求Bayes总则判别函数，并对样本39，40，41分类。第八章习题：1证明主成分载荷 （i=1,2,.,p;k=1,2,m）是主成分与变量之间的相关系数2以两个变量主成分为例证明主分量 和 是无关的（正交）。3.证明p个主分量的总方差与原p个变量的总方差相等4. 对下表数据进行如下操作（1）.求前三个主成份得分系数距阵（2）.写出各变量的因子表达式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某地区35个城市2004年的7项经济统计指标数据见下表。（1）试用最短距离聚类法对45个城市综合实力进行系统聚类分析，并画出聚类谱系图；（2）试用主成分分析法对45个城市7项经济指标进行主成分分析，并分析其综合实力；（3）以第一、二、三主成分为变量，进行聚类分析，结果又怎样呢？城市编号总人口(单位：104人)非农业人口比例(单位:%)农业总产值(单位：108元)工业总产值(单位：108元)地方财政预算内收入(单位：108元)城乡居民年底储蓄余额(单位：108元)在岗职工工资总额(单位：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