无约束重力模式根据无约束重力模型公式：两边取对数得Ln(Tij)=lnk+αlnGi+βlnAj-γlntijTij─交通区i到交通区j的出行分布量：Gi─交通区i的出行产生总量：Aj─交通区j的出行吸引总量：K，α，β，γ─模型参数；公式转换为:Y=K+αx1+βx2-γx3参数的确定是通过拟合现状OD调查资料，用最小二乘法确定。现有一规划区域，共划分为5个交通区，经调查其现状OD分布见表1，各交通区间的出行时间见表2，通过对各交通区的交通生成进行预测，得到各交通区未来交通产生、吸引量见表3，分析计算得到未来各交通区间的交通出行时间见表4。表A1（现状OD分布）交通区1234518006002003004002200210050020015054502409001005041101002407005059050100120600表B2（各交通区间的出行时间）交通区123451510182030212410252031510815354202515103053525353512表C2（各交通区未来交通产生，吸引量）交通区产生量吸引量152004400245004100333003400421002700523002200表D1（未来各交通区间的交通出行时间）交通区1234515101215202104820203101071030415201082053020303010解：选用出行时间的函数形式，将无约束重力模型变为：Ln(Tij)=lnk+αlnGi+βlnAj-γlntij格式LN(number)：number是用于计算其自然对数的正实数。Ln是exp函数的反函数计算步骤：打开数据文件，在定下的单元格中输入公式Ln(number),按下number之后选择要计算的数字，然后按下Entre键后公式将返回计算结果如下表：ijTGATlnTlnGlnAlnt118005200440056.6846128.5564148.389361.6094381260052004100106.396938.5564148.3187422.3025851320052003400125.2983178.5564148.1315312.4849071430052002700155.7037828.5564147.9010072.708051540052002200205.9914658.5564147.6962132.9957322120045004400105.2983178.4118338.389362.3025852221004500410047.6496938.4118338.3187421.386294235004500340086.2146088.4118338.1315312.0794422420045002700205.2983178.4118337.9010072.9957322515045002200205.0106358.4118337.6962132.9957323145033004400106.1092488.1016788.389362.3025853224033004100105.4806398.1016788.3187422.302585339003300340076.8023958.1016788.1315311.945913410033002700104.605178.1016787.9010072.302585355033002200303.9120238.1016787.6962133.4011974111021004400154.700487.6496938.389362.708054210021004100204.605177.6496938.3187422.9957324324021003400105.4806397.6496938.1315312.302585447002100270086.551087.6496937.9010072.079442455021002200203.9120237.6496937.6962132.995732519023004400304.499817.7406648.389363.401197525023004100203.9120237.7406648.3187422.9957325310023003400304.605177.7406648.1315313.4011975412023002700304.7874927.7406647.9010073.4011975560023002200106.396937.7406647.6962132.302585YX1X2X3Y=K+αx1+βx2-γx3此方程为线性回归方程，k,α，β，γ是用最小二乘法标定。计算步骤：[c¹·c]¯¹c¹·y=β^c=(1x)：YX1X2X36.684618.55648.38941.60946.396918.55648.31872.30265.298318.55648.13152.48495.703818.55647.90102.70815.991518.55647.69622.99575.298318.41188.38942.30267.649718.41188.31871.38636.214618.41188.13152.07945.298318.41187.90102.99575.010618.41187.69622.99576.109218.10178.38942.30265.480618.10178.31872.30266.802418.10178.13151.94594.605218.10177.90102.30263.912018.10177.69623.40124.700517.64978.38942.70814.605217.64978.31872.99575.480617.64978.13152.30266.551117.64977.90102.07943.912017.64977.69622.99574.499817.74078.38943.40123.912017.74078.31872.99574.605217.74078.13153.40124.787517.74077.90103.40126.396917.74077.69622.3026将C=(1x)转置的步骤是：按矩阵c选择行列数，在单元格中输入:=TRANSPOSE(B2:E26)，然后按Cntrl+Shift+Enter组合键最后得出的结果是如下表（C¹）:11111111111111111111111118.5564148.5564148.5564148.5564148.5564148.4118338.4118338.4118338.4118338.4118338....
