Seattle Department of Transportation counts the number of bicyclists at each of

Question

Seattle Department of Transportation counts the number of bicyclists at each of 50 locations through- out the city. Bicyclists are counted in each of an evening peak commute time (PM peak, 5-7 pm), an off-peak time (10 am 12 noon and a Saturday time period (noon 2 pm). The following shows the first 5 lines (out of 50) of the data for July 2012. The Saturday entry for Station 2 is missing and marked as NA here. site ID Location Off Peak PM Peak Saturday T1 Linden Ave N and N 130th St 20 16 53 Greenwood Ave N and N 85th St 12 14 NA 3 NE Ravenna Blvd, E Green Lake Way N/NE 71st St 60 149 95 32nd Ave NW and NW 54th St 31 39 62 5 NW Market St and 24th Ave NW/Shilshole Ave NW 56 All 50 rows of data were read into a data frame labeled "2012.July". Consider the following R code, and answer the subsequent questions. Note that the summary results for each model fit indicate that one row of data was omitted during model fitting, due to missingness corresponding to the row containing the NA above. names 2012. July) [1] "ID" "Location "Off Peak "PM. Peak" "Saturday Total

Explanation / Answer

(b)

For the ID 2, the estimate of the number of bikes passing the location is

3.0874 + 12*0.0115 + 14*0.0014 = 3.245

(c) (I) The hypothesis being tested is that the H: P1 = P2, where P1 and P2 are the two probability distributions. The theoretical test statistic is the chi-square test statistic and the approximate distribution is the chi-square distribution.

(ii) It is not possible to carry the test as the data set is not available.

(d) The assumption of fit2 is that the number of bikes passing the location follows a Poisson distribution. It is a reasonable assumption and has bee applied in many such example.

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