Trip purpose by time of day trip purpose by time of

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Trip Purpose by Time of Day Trip Purpose by Time of Day 62% 23% 60% 15% 48% 0 500 1000 1500 2000 2500 12:00 AM 2:00 AM 4:00 AM 6:00 AM 8:00 AM 10:00 AM 12:00 PM 2:00 PM 4:00 PM 6:00 PM 8:00 PM 10:00 PM 12:00 AM Commute to work from home Commute from work to home Travel to/from school Travel to/from airport Personal business/Work related Shopping/Recreation Total
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Estimating Trip Generation Models Estimating Trip Generation Models The first traveler decision to be modeled in the sequential approach to demand forecasting is trip generation Trip generation models generally assume a linear form.
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Consider the following hypothetical trip generation data : A. Simple Linear Regression Household No. 1 2 3 4 5 6 7 8 9 i Number of shopping trips made all day Saturday Y i 3 1 1 5 3 2 6 4 5 2 10 People in Household i X i 4 2 3 4 2 4 8 6 6 2 y = 3.2 x = 4.1
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Objective: predict No. of Shopping trips made on Saturday for each household, dependant variable, y i Function of the number of people in HH, x i , independent variable (This is the Calibration Phase) A simple linear relationship i o i x b b y 1 + = We need to determine the coefficient b o & b 1
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0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 People in household Xi S h o p p i n g t r i p s y i Assume b o = 1.5 b 1 = 0 no relation between y i & x i Deviation = y i - (b o +b 1 x i ) observed predicted
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0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 People in household Xi Shopping trips yi Assume b o = 1.5 b 1 = .5 here, deviations are reduced
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So we need to determine b 0 & b 1 that produce the smallest possible deviations. we minimize the sum of squares of deviations (least square regression) Min. y (b o , b 1 ) = i i o i x b b y 2 1 ) (
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Setting partial derivatives to zero 0 ) ( 2 0 ) ( 2 1 1 1 = = = = i i o i i i i o i o x b b y x b y x b b y b y 0 0 2 1 1 = = i i i i o i i i i i o i i x b x b y x x b nb y
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Where n is the total number of observations (in this case HHs) Solving the two equations ( ) ( ) ( ) x b y b x x y y x x b o i i i i i 1 2 1 = = Using the data that we have i i x y 7 . 0 33 . 0 + =
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Multiple Linear Regression It is usually appropriate relationships that include more than one independent variable n n o x b x b x b b y + + + + = .... ..........
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  • Spring '10
  • EssamRadwan
  • Regression Analysis, Household income in the United States, Trip generation, household Xi

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