Transport Data Analysis: Quantitative Analysis - Assignment Example

Quantitative Analysis Name of the student Name of the Institution Date of Submission Introduction Qualitative data aimed at making inferences from the available information given by the researcher. This paper aimed at making inferences concerning data collection, its reliability and performing statistical analysis when it comes to qualitative data. The data to be analyzed is in reference of vehicle pollutant. It aimed at finding out if a particular vehicle is a gross polluter on not is necessary to drive behind the vehicle of interest for approximately ten seconds. Question one Q1(1) Yes the observation is independent A sample can be described as a subset of the total population which has been selected for study. Sampling on the other hand can be described as the process of selecting the sample from the whole population for study purposes (van Boeke et al., 2015). Therefore sampling strategy can be defined as the techniques that have been employed to ensure that the sample you are going to use for study research is all inclusive and represent the intended population of study (Masters et al., 2015). There are different types of sampling techniques they include Probability sampling: - it includes some form of random selection in choosing the elements to be used in the study (Masters et al., 2015) Using this method, greater confidence can be placed in the data representativeness. The kind of sampling involves selection process in which each element of study has an equal chance and independent chances of being selected to participate in the study. Using probability sampling, the observation is independent and lacks biasness and will give realistic in terms of the amount of sample given. (Masters et al., 2015) states that 10% of the population is good sample and gives a full representation of the data. If 20 vehicle can be tested every tested per hour gives good representation of the data (van Boeke et al., 2015). Q1(2) From the information given, the data will be enough for marking valid conclusion concerning the data since it is all inclusive and meets the target value of the study. Having 100 vehicles per hour passing the station, 20% of the total population is good for doing the analysis as it will give both models types and hours are evenly presented in the data. This data will be adequate to help in hypothesis test due to its representativeness of the information concerning the vehicle types. In any study, the chosen sample is very important to the overall research work. The questions and hypothesis may be great, but based on the sample one is able to make inferences concerning the differences you found from the analysis (Masters et al., 2015). Qualitative data requires qualitative data sampling strategy and this very critical when it comes to time series data (van Boeke et al., 2015). Q1(3) When having a total salary and wage expenses of $500, to optimize means to modify some of the aspect so that it can be efficiently used in the process. The wages can be optimized by reducing the traffic jams and fare collection process. Optimization can also means reduction of the number of people who are working at any given time so that it can result to more lean and efficient number of people in place. Some of the tradeoffs include laying off of excess workers which may result to unemployment hence leading to the reduction in work force. Secondly, trade off can lead to employed a more sophisticated technology which may result to additional expenses to the firm. Increased cost means reduction of the profits hence overall benefit for short run. Thirdly, it can lead to hiring more experience manpower to manage technological changes in the organization this will further result to a more expensive man power which might prove more costly to the firm. Question two 1a. Use SPSS to perform ANOVA Anova: Single Factor SUMMARY Groups Count Sum Average Variance Test Mass 124 283183 2283.734 124492.5 CUEDC_FC 124 2004.931 16.1688 7.362703 DT80_FC 124 2623.254 21.15528 13.54362 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4.24E+08 2 2.12E+08 5109.413 1.1E-269 3.020185 Within Groups 15315154 369 41504.48 Total 4.39E+08 371         1b. Check assumptions required for ANOVA Using ANOVA, there are two types of assumptions, validity and distribution assumptions The systemic error is normally called bias; lack of bias in analysis is normally called validity in statistical analysis three major validity assumption include No selection bias No information bias Comparability of groups when comparing the effect of an exposure ANOVA distribution includes; Independence of observations within and between samples Normality of sampling distribution Equal variance 2a. Determine correlation coefficient for vehicle mass and fuel consumption to find out the degree of linear correlation between these two random variables Test Mass CUEDC_FC DT80_FC   2275 15.45674 17.0075 Test Mass 2275 1 CUEDC_FC 15.45674 0.652733 1 DT80_FC 17.0075 0.646612 0.876424 1 2b. Develop linear regression model by using SPSS SUMMARY OUTPUT Regression Statistics Multiple R 0.652601 R Square 0.425888 Adjusted R Square 0.421182 Standard Error 268.4372 Observations 124 ANOVA   df SS MS F Significance F Regression 1 6521439 6521439 90.50196 2.17E-16 Residual 122 8791143 72058.55 Total 123 15312582         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 911.6573 146.2286 6.234465 6.75E-09 622.1831 1201.131 622.1831 1201.131 CUEDC_FC 84.85951 8.920138 9.513252 2.17E-16 67.20121 102.5178 67.20121 102.5178 The model in form of Y = ax + c = 911.6673x + 84.86 2c. check the assumptions required for simple linear regression model In the analysis of linear regression the following are the assumptions Each value of X1 & Y is observed without error measurement Relationship between dependent and independent variables are linear Each conditional distribution of a has a mean zero The variance of the conditional distribution of u is constant for all such distribution The value of u is serially independent The independent variable are linearly independent of each other 2d. Discuss the output from SPSS From the ANOVA test, there is sufficient information to conclude if the average fuel consumption of new vehicle varies for different year categories since the p-value is greater than F-statistics indicating that it is statistically significant. The bigger variance between the two values is further proving that the consumption between the two models is different. From the correlation output in the table above, there are positive correlations between the variables. From the output, 1% increase in Test mass results into 65.27% increase in fuel consumption CUEDC model while it result into 87.64% increase in fuel consumption of DT80 model. 3. Are fuel consumptions obtained by CUEDC and DT80 tests significantly different? SUMMARY OUTPUT Regression Statistics Multiple R 0.669706 R Square 0.448506 Adjusted R Square 0.439391 Standard Error 264.1812 Observations 124 ANOVA   df SS MS F Significance F Regression 2 6867788 3433894 49.20205 2.31E-16 Residual 121 8444794 69791.69 Total 123 15312582         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 852.6494 146.3276 5.826988 4.77E-08 562.9552 1142.344 562.9552 1142.344 CUEDC_FC 49.68031 18.06783 2.749656 0.006881 13.91027 85.45034 13.91027 85.45034 DT80_FC 29.67645 13.32163 2.22769 0.02775 3.302775 56.05012 3.302775 56.05012 4a. Develop regression model for the relationship between the two fuel consumptions SUMMARY OUTPUT Regression Statistics Multiple R 0.874028 R Square 0.763925 Adjusted R Square 0.76199 Standard Error 1.323781 Observations 124 ANOVA   df SS MS F Significance F Regression 1 691.8203 691.8203 394.7856 4.69E-40 Residual 122 213.7922 1.752395 Total 123 905.6125         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.535673 0.696365 3.641297 0.000399 1.157148 3.914198 1.157148 3.914198 DT80_FC 0.644432 0.032434 19.86921 4.69E-40 0.580226 0.708637 0.580226 0.708637 4b. Find the confidence interval for the predicted fuel consumption for a vehicle that have DT80_FC equal to 20 /100 km Using the model from the regression, The model in form of Y = ax + c 20/100 = 2.5x + 0.64 2.5x = 0.2 – 0.64 2.5x =- 0.44 X = -0.44 /2.5 = -0.176 Question3 Q3 (1) Graph traffic flow by hour of day separately for each of the three days. State the main differences between what happens on the road. At a more detailed level, in what way do the flow patterns differ? Day 2 Day 3 Day4 From the graphs in the three different days, day 2 and day 3 flow of traffic is the same while on day 4 is different. The main different between the three graphs I the smoothness of the traffic flow. The first two graphs have smooth flowing pattern while the third graph in day four is having seasonal kind of movement that is speed changes with time. Q3 (2). Graph mean speed by hour of day separately for each of the three days. Comment, as in 1. Day 2 Day 3 Day 4 The three grwph have different shapes with the day one graph having ups and downward movement at different point. This shows that mean value of three graphs are all different . on the graph the mean was lowest at speed that is point 4 while highest at point five which is headway. Q3 (3) Graph standard deviation of speed and headway by hour of day for those days on the same graph. Explain the differences Day2 Day 3 Day4 The differences in the three graphs of standard deviation show different changes in speed and headway. The different is further indicated in the shape of the graphs with troughs and ups. Q3 (4) Graph mean free flow speed by hour of day for each of the three days. Comment briefly in relation to hourly means of all speeds. Day2 Day3 Day4 The three graphs shows positive relationship between mean speed and hourly basis and it is linear while in the third graph shows negative relationship however it remains linear throughout. Q3 (5) Calculate the percentage of speeds that are free flow on those days, time of day and give you views on the fact. By referring to hourly counts and hourly mean speeds, is there evidence of congestion during either of the peak periods? At the free flow rate the percentage speed is equivalent to the slope of the graph this can be calculated using Pythagoras theorem. It is given by (change in speed squared plus change in hours squared) squawroot = (502 + 102) = 604 squawroot = 24.57 There is high rate of congestion during the peak as can be shown in the graphs and using the squawroot. Q3 (6) It might be expected that the proportion of vehicles with free flow speeds falls as traffic volumes rise (use another day’s data to test this). Here you may try CHI square test to test this hypothesis. If you restrict the test to the daylight hours (07:00 to 17:00), do you get a similar result? First test- T-test t-Test: Paired Two Sample for Means   0 69.5 Mean 14.779577 62.23597 Variance 20.73107123 27.90243 Observations 9078 9078 Pearson Correlation -0.107791212 Hypothesized Mean Difference 4 df 9077 t Stat -668.2958453 P(T Read More

Qualitative data requires qualitative data sampling strategy and this very critical when it comes to time series data (van Boeke et al., 2015). Q1(3) When having a total salary and wage expenses of $500, to optimize means to modify some of the aspect so that it can be efficiently used in the process. The wages can be optimized by reducing the traffic jams and fare collection process. Optimization can also means reduction of the number of people who are working at any given time so that it can result to more lean and efficient number of people in place.

Some of the tradeoffs include laying off of excess workers which may result to unemployment hence leading to the reduction in work force. Secondly, trade off can lead to employed a more sophisticated technology which may result to additional expenses to the firm. Increased cost means reduction of the profits hence overall benefit for short run. Thirdly, it can lead to hiring more experience manpower to manage technological changes in the organization this will further result to a more expensive man power which might prove more costly to the firm.

Question two 1a. Use SPSS to perform ANOVA Anova: Single Factor SUMMARY Groups Count Sum Average Variance Test Mass 124 283183 2283.734 124492.5 CUEDC_FC 124 2004.931 16.1688 7.362703 DT80_FC 124 2623.254 21.15528 13.54362 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4.24E+08 2 2.12E+08 5109.413 1.1E-269 3.020185 Within Groups 15315154 369 41504.48 Total 4.39E+08 371         1b. Check assumptions required for ANOVA Using ANOVA, there are two types of assumptions, validity and distribution assumptions The systemic error is normally called bias; lack of bias in analysis is normally called validity in statistical analysis three major validity assumption include No selection bias No information bias Comparability of groups when comparing the effect of an exposure ANOVA distribution includes; Independence of observations within and between samples Normality of sampling distribution Equal variance 2a.

Determine correlation coefficient for vehicle mass and fuel consumption to find out the degree of linear correlation between these two random variables Test Mass CUEDC_FC DT80_FC   2275 15.45674 17.0075 Test Mass 2275 1 CUEDC_FC 15.45674 0.652733 1 DT80_FC 17.0075 0.646612 0.876424 1 2b. Develop linear regression model by using SPSS SUMMARY OUTPUT Regression Statistics Multiple R 0.652601 R Square 0.425888 Adjusted R Square 0.421182 Standard Error 268.4372 Observations 124 ANOVA   df SS MS F Significance F Regression 1 6521439 6521439 90.50196 2.17E-16 Residual 122 8791143 72058.

55 Total 123 15312582         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 911.6573 146.2286 6.234465 6.75E-09 622.1831 1201.131 622.1831 1201.131 CUEDC_FC 84.85951 8.920138 9.513252 2.17E-16 67.20121 102.5178 67.20121 102.5178 The model in form of Y = ax + c = 911.6673x + 84.86 2c. check the assumptions required for simple linear regression model In the analysis of linear regression the following are the assumptions Each value of X1 & Y is observed without error measurement Relationship between dependent and independent variables are linear Each conditional distribution of a has a mean zero The variance of the conditional distribution of u is constant for all such distribution The value of u is serially independent The independent variable are linearly independent of each other 2d.

Discuss the output from SPSS From the ANOVA test, there is sufficient information to conclude if the average fuel consumption of new vehicle varies for different year categories since the p-value is greater than F-statistics indicating that it is statistically significant. The bigger variance between the two values is further proving that the consumption between the two models is different. From the correlation output in the table above, there are positive correlations between the variables.

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