Multiple Regression and Structural Equation - MyAssignmenthelp.com

Question: Discuss about the Multiple Regression and Structural Equation Modelling. Answer: Introduction: Automotive CO2 emission is one of the major concerns in the contemporary world, where researchers and countries are trying to reduce the level of carbon emitted to the atmosphere. The main concern in reducing the emission of carbon dioxide is to protect the ozone layer, whose destruction is causing a lot of harm to the global climate change. Government and non-governmental organizations have invested much to ensure that activities and phenomena which produce more carbon dioxide among other dangerous gases embrace newer technologies. The automobile research for carbon emission is aimed to study the rate of the dangerous gas to the atmosphere. Automotive being one of the major sources of CO2, the involved parties have focused their concerns on the level of carbon a vehicle emits as a result of fuel combustion. It has been the thought of the scientists in charge of monitoring and evaluation of the acceptable emission of CO2 that vehicles should have a general limit. This force has been moved to the car manufacturers to ensure that their automotive vehicles emit the least possible amount of carbon to the environment. Policies and rules have been developed to govern the acceptable level of carbon emission into space. Automobiles are not the only producers of carbon dioxide; burning of rubber and plastics also contribute significantly to the demolition of the ozone layer. This paper will focus on analyzing automobile data that was generated based on different vehicles with their corresponding CO2 emissions among other characteristics. Moreover, I will be acting as a data analyst intern, focusing on answering some questions usi ng basic analytical methods. Overall View of CO2 Emissions Fuel Type Mean count Percent 1 233 518 47.87% 2 256 466 43.07% 3 220 35 3.23% 4 268 63 5.82% Based on the Automotive CO2 emissions data obtained from a recent study, it has been found that an average vehicle emits 250 grams of carbon dioxide per kilometer. In this case, a car that is chosen at random in the population, there is a higher chance that it emits carbon dioxide amounts that are close to 250 grams per a kilometer. The data indicates that the highest level of carbon dioxide emitted by a car was 437 grams per kilometer compared to the least which was 108. However, this indicates that the most extreme levels of carbon dioxide emission per kilometer are around 430 gram per kilometer. Manufacturers of automobiles should make the carbon emission per vehicle as low as possible. This has been a hard task because they have to balance between the performance and the amount of power a car requires. The power used by a vehicle is equivalent to the amount of carbon dioxide emitted to the atmosphere. This show a high variation of the CO2 emission from the average car emission, which indicates that automotive production can still be modified to produce cars that produce low amounts of carbon. Since the data is highly spread, it might be hard to use the information in predictions. The type of fuel a car uses determines the amount of carbon dioxide to be emitted after the combustion. It is also possible that a car uses a lot of fuel but is not equivalent to the amounts of carbon emitted based on the quality. Some automotive vehicle manufacturers have embraced renewable energies which have low amounts of carbon as compared to the others. This is because the differences in the fuels are based on their qualities, which is quantified in terms of carbon levels. After the analysis, it was found that cars that were using fuel type three emitted the least average amounts of carbon compared to fuel type 4, whose vehicles emitted the highest amounts. However, most individuals preferred fuel type one assuming that the data was randomly collected from the population. Therefore, it can be concluded that the fuel type was related to the levels of CO2 emissions for the specific vehicles (Fox, 2015). Confidence Intervals for CO2 for different Engine Cylinders The number of cylinders that a car had also been determinants on the level of carbon dioxide would be emitted. This is because the higher the counts of cylinders indicate that the vehicles requires a lot of power, hence increased levels of combustion. More combustion indicates more emission of carbon dioxide to the environment. Based on the analysis, there has been identified a significant difference between the three groups; four (4), six (6) and eight (8) cylinders based on their emissions. Vehicles having a fewer number of cylinders in their engines seems to emit fewer amounts of CO2 compared to the others. These statistics indicate that there is a positive correlation between carbon dioxide emissions and the size of the engines. The engine size is quantified based on the number of cylinders available; whereby there are 4, 6 and 8 cylinders. Therefore, the average emission of carbon dioxide for the cars that has engines with 4 cylinders would be contained in 199.213 to 202.623 bound with a 95 percent confidence. This interval was a bit lower compared to the vehicles with 6 and 8 cylinders whose bound is 256.528 to 259.836 and 319.719 to 324.893 respectively. Therefore, if the study was repeated several times, their respective means of the carbon dioxide emission would lie within the indicated intervals 95% of the times. These inferential statistics can be used in estimating the amounts of carbon dioxide emitted by automobiles observed in the same setting. Although the automobile manufacturing seems to be produced under the same conditions, which makes it possible to generalise study over the globe irrespective of where the data originated. Proportions of Different types of Engine Cylinders Most of the vehicles in the population has vehicles with 4 cylinder engine with a proportion of 0.452, which accounts for almost half of the population. The six and eight-cylinder vehicles occupy a proportion of 0.355 and 0.193 respectively. These proportions show that most of the people in the population prefer vehicles with engines that have 4 cylinders because of their personal requirements, price constraints or even the conditions of their environment. Repetition of the study in the same setting would a generate data that at 95% confidence produces a proportion of 4 cylinder vehicles between 42.23% and 48.16%. In addition, I am confident stating that the proportion of 6 cylinders and 8 cylinders would lie within 32.64% to 38.34% and 16.96% to 21.67% respectively with a 5% error. The confidence interval for the population proportions shows the upper and lower bounds that can be obtained for the same study using the same targets. Vehicles emitting more than 350 grams per kilometre accounts for 0.0388 of the population based on the sample data. This proportion was used in estimating whether the vehicles emitting more than 350g/km constitute of 5% of the population. One proportion test was conducted and a p-value of 0.0465 was obtained an indication that the proportion of vehicles emitting more than 350 grams per kilometres were more than 5%. Therefore, the data supports that restricting vehicles emitting more than 350g/km would reduce the population of largest polluting by 5%. The proposal should be accepted to enhance the reduction of pollution by these types of vehicles in the environment (Schi, Tao, 2008). The best way to reduce pollution in the environment is by concentrating on the main contributors, which reduces by the high rate. Regression between Engine Size and CO2 Emission The emission level of engines is highly dependent on its size. There is a strong positive correlation between the size of an engine and the amount CO2 emitted, which indicates that the larger the engine, the higher the level of carbon emission. This is according to the expectation of direct relationship between the two variables. The Pearsons Correlation coefficient between the two variables; CO2 emissions and engine size are 0.8376, which shows a high level of relationship (Anderson, 2017). The size of the engine is a good indicator of the level of carbon dioxide emission for a vehicle and it can be used in a model to make predictions. Moreover, the linear relationship between engine size and carbon dioxide emission is very strong, indicating that a high number of cylinders increases emission. Therefore, the high correlation meets a regression requirement for the relationship. The size of car engine variable in the sample data set was use in model development. It was observed that 70.16% of the variations experienced in the level of carbon dioxide emission could be explained using the size of the car engine. Therefore, for every one-litre increase in the size of the engine, the level of emission would be increased by 39.594. In addition, it can be explained that engine size and the level of carbon emission for a vehicle are proportionally directly related. This model which includes the engine size as the predictor and CO2 emission as the response variable is highly significant at 5% level. Maintaining the same factors in the model, the intercept will be contained in 125.51 to 135.13 interval with a 95% confidence. Similarly, the engine size coefficient within the model will also be contained in the range 35.17 to 38.02 (Hilbe, 2013). In sampling, statistical inference and modelling, the results can only be inferred to the population that was fairly represented. According to the distribution of the data, there was not much information about cars that have engines of 1 litres size. Therefore, a lot of errors might be obtained in trying to predict the amount of carbon dioxide emitted using the model that does not adequately represent this types of cars. In this cases, this model will not be used in making prediction for cars with engine size that is not represented in the data (Seber, Lee, 2012). Appropriate Sample Size The proportion of vehicles that were emitting more than 350 grams per kilometre in the sample was 0.96. I am confident that the proportion of vehicles contributing to high levels of pollution (350 grams of carbon dioxide per kilometre) would be included in the range between 94.84% and 97.39. In addition, the average of fuel consumption for all the vehicles was 10.89 litres per 100 kilometres. The variation within the fuel consumption data from the average value was around 2.9 litres of fuel per 100 kilometres. Therefore, I am confident that if the study was repeated severally, the average usage of fuel per 100 kilometres will lie within 10.72 and 11.06 litres (Newbold, Carlson, Thorne, 2013). There are several factors that are considered in determining the size of a sample for any specific study. Some of these factors include the availability of the resources such as time, money and human resources. The nature of the study is also another main factor, which is mainly considered by professional researchers and coordinators. For instance, a study associated with rare conditions would require a large sample to enhance the chances of detecting a case. In some occasions, proportional allocation is also factored to ensure that the units are included in the population based on their distribution in the target population. Therefore, if all these factors are considered, the best sample size will be determined, which is able to provide the best results for the study (Keith, 2014). Conclusion In conclusion, carbon dioxide emission should be reduced by manufacturing cars that are more reliable and friendly to the environment. Also, the government should develop policies which instil restrictions to the acceptable levels for carbon emission for an automobile. In this way, the pollution rate will be reduced, hence creating a better environment that is conducive for every person. Based on the above analysis, it has been found that vehicles with smaller engine size emit less carbon dioxide. Therefore, manufactures should concentrate on developing smaller engines. Finally, a reliable prediction model should be developed by including data from all available different engine sizes, so that can it be used in general prediction. References Anderson, D. (2017). Modern business statistics with Microsoft excel (1st Ed.). Cenge Learning Custom P. Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications. Hilbe, J. (2013). Methods of Statistical Model Estimation (1st Ed.). Hoboken: CRC Press. Keith, T.Z., 2014. Multiple regression and beyond: An introduction to multiple regression and structural equation modelling. Routledge. Newbold, P., Carlson, W., Thorne, B. (2013). Statistics for business and economics (1st Ed.). Boston: Pearson. Schi, N., Tao, J. (2008). Statistical hypothesis testing (1st Ed.). Singapore: World Scientific. Seber, G., Lee, A. (2012). Linear Regression Analysis (1st Ed.). Hoboken: Wiley.