Regression model for traffic survey An Origin-Destination survey in ten zones pr
ID: 1920719 • Letter: R
Question
Regression model for traffic survey
An Origin-Destination survey in ten zones provides the following data relating to Zonal residential density, X given in households/hectare and average daily car trips productions (Y) per household Calibrate a regression model of the form of Y = A + BX Calibrate a regression model of the form of Y = a + b Loge X Estimate the number daily car trips that would be expected to generate form a zone having 4500 household in 1800 hectares, using the models developed in (a) and (b) above Log, X = In X; Shower calculations of all parameters such as A, B, a & b. Round the value of these model parameters closer to three decimal places (i.e., if your value is 5.235173456 then you value should be 5.235)Explanation / Answer
Sl no Y X ln X X-Mean(X) Y-mean(Y) ln X-mean(ln X) (X-Mean(X))^2 (ln X-mean(ln X))^2 (X-meanX)(Y-meanY) (LnX-mean(ln X))(Y-meanY) 1 1.5 42 3.738 25.1 -1.160 1.121 630.01 1.256 -29.116 -1.300 2 4 5 1.609 -11.9 1.340 -1.008 141.61 1.015 -15.946 -1.350 3 2.1 25 3.219 8.1 -0.560 0.602 65.61 0.362 -4.536 -0.337 4 2.6 10 2.303 -6.9 -0.060 -0.314 47.61 0.099 0.414 0.019 5 4.8 4 1.386 -12.9 2.140 -1.231 166.41 1.515 -27.606 -2.634 6 2 15 2.708 -1.9 -0.660 0.091 3.61 0.008 1.254 -0.060 7 2.4 20 2.996 3.1 -0.260 0.379 9.61 0.143 -0.806 -0.098 8 3.3 12 2.485 -4.9 0.640 -0.132 24.01 0.017 -3.136 -0.085 9 1.9 14 2.639 -2.9 -0.760 0.022 8.41 0.000 2.204 -0.017 10 2 22 3.091 5.1 -0.660 0.474 26.01 0.225 -3.366 -0.313 total 26.6 169 26.174 1122.900 4.641 -80.640 -6.175 mean 2.66 16.9 2.617 For (a) For (b) Y-mean(Y) = slope (X-mean(X)) Y-mean(Y) = slope (X-mean(X)) slope = sum((X-meanX)(Y-meanY) / sum((X-Mean(X))^2) slope = sum((ln X-mean(ln X))(Y-meanY) / sum((ln X-Mean(ln X))^2) slope = -80.640 / 1122.900 = -0.072 slope = -6.175 / 4.641 = -1.331 Y-2.66 = -0.072 (X-16.9) Y-2.66 = -1.331 (ln X-2.617) Y = 3.877 - 0.072 X Y = 6.143 - 1.331 ln X For (c ) ln X = Ln 2.5 = 0.9163 Resn Density = 4500/1800 = 2.5 Y = 6.143 - 1.331*0.9163 = 4.923 Y = 3.877 - 0.072*2.5 = 3.697
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