Energy fuel consumption- Statistic Project by using ANOVA table and Hypothesis
INTRODUCTION
There is a lot to learn about the energy fuel consumption in Canada. Rather, the energy fuel consumption has got a list of salient features so as to find out the profits generated from this consumption. Canada is one of the largest energy producers and exporters of products in the world.
The project aims at calculating the connection between different variables related to energy fuel consumption in Canada. Owing to my immense interest in learning about this field, I have collected a lot of raw material I have had a lot of interest in learning about the energy consumption industry in Canada as it is not as big as many Asian countries. This data and research will definitely help me learn about the energy consumption in Canada and gather some interesting facts.
Using energy produced from fossil fuels : The usage of carbon fuels and the related production of energy can be estimated from a couple of different perspectives. In case of atmospheric emissions, it is useful to identify which sectors are truly consuming carbon fuels which yields emissions. According to this, fuels used by electricity generation are directed completely to that sector although a majority of energy gets transformed to electricity.
Energy produced from renewable energy sources is included in the total sectoral breakdown and is also presented separately as an aggregated total. The renewable sources of energy includes solar power, wave and tide, energy from wood, straw, sewage gas and hydroelectricity. In context of sustainable development policy, municipal solid waste combustion are also renewable energy sources.
The energy fuel consumption has had its own bust and boom in the last few decades, ranging from famines to very good times. In this project we will be using ANOVA analysis and similar hypothesis to find out the few significant variables which determine the corporation profits. The coefficient of determination will help us decide the goodness of line. We will also forecast the next 3 years corporation profits after getting the most appropriate estimated results.
With the U.S chemical industry being the largest in the world, U.S counts for 11% of the industrial production as the value addition. It constitutes the 20% total energy consumption in the U.S and also counts for similar proportions of greenhouse emissions. Unfortunately, there is not much info available on the energy consumption in the available chemical industry. The report ahead provides a detailed info on usage of energy for the energy intensive chemical products for the major groups. The major product in terms of ethylene production in terms of production volume of the petrochemical industry. There are a wide variety of products in the petrochemical industry. Most of the energy produced is dedicated for a small number of mediate compounds, of which ethylene is most significance. Use of primary energy use by Carbon dioxide emissions from the U.S. chemicals Is approximately 20% of the overall primary energy usage. The produced chemical energy counts for 11% of the value added in the U.S With an increase in annual growth rate of 2.9%, the value added has increased at a rapid rate of 4.6%.
Complete energy consumption for a few chemical subsectors is provided by the U.S manufacturing energy consumption survey. There are a few subsectors which account for a huge share of primary energy in 1994. These include resins, industrial gases, chlorines, alkalies and other materials. Resins and plastics being an exception, the primary energy requirements of the energy production. There are a couple of high energy intensive production procedures which are used to produce intermediate chemicals.
ANOVA Method
The Annova technique evaluates the presence or absence of a statistical difference between the mean of two or more data groups. For instance, when there is data related to student performance, one is more interested in checking the tutorial performance. ANOVA makes it possible to break up the group as per the grade and then check if the performance. The ANOVA technology is available for both non parametric and parametric information. There are a wide variety of ANOVA. These include:
The ANOVA is the simplest version where one grouping is used to define the groups. This category of ANOVA is used to compare variables between different groups. When there is a single group which has been measured a couple of times, a one way repeated measure is used. For instance a one way repeated measure ANOVA is used to check if the performance in the test changed with time. In order to view the complex groupings, a two-way between groups ANOVA is used. ANOVA is used for score or interval data as parametric ANOVA. Where a categegorical data is used, ANOVA method is not used and one has to make use of Chi-square which is related to interaction between several groups. There is a nonparametric test which is found under the heading non parametric version.
ANOVA is basically used to calculate the mean for each final grading groups on the basis of the Group Means. It is also used to calculate the mean of all the combined groups also known as the overall mean. Post overall mean, the total deviation of each individual score from the group mean also known as within group variation. Also, a between group variation is calculated within every group and the difference of each group mean from the overall mean is calculated also known as the between group variation. Just in case the between group variation is higher than the within group variation, a statistally significant difference between the groups is calculated. The package of the statistics tells one whether the F ratio is important or not. There are a fixed number of basic principles and versions of ANOVA, the sources of variation take a more complex form as the number of groups increases and there interaction effect intensifies.
OBSERVATIONS
Statistical Methodology:-
The following project makes use of the statistical ideas which include:
- F test and t test
- Test statistics and forecasting
The F test and T tests:
The aim of F test in a multiple regression analysis is to test the importance of independence variables in case of a multiple regression model. It is basically a statistical test for comparing different variance measures in more than two groups. Out of these two, one statistic measures the variations between the means of the groups while the other measures the variations within the groups, also known as the residual. If the two measures of variance yields same outputs, the ratio F-ratio equals 1.0 approximately. In this case the null hypothesis that all the population cannot be directly ignored. On the other hand, under the alternative hypothesis, the F-ratio is usually more than 1.0. The analysis of variance is used for conducting the test of importance of regression in case of multiple linear regression theory. The test is mainly used to ensure that if a linear statistical relation persists between the response variable and any one of the predictor variables.
The statements for the hypotheses are:
Ho:- B1=B2=B3=B4=B5=b6
Ha:- Not all the means are equal.
The test for Ho is carried out using the following statistic:
Fo= MSR/ MSE
Where, MSR is the regression mean square and MSE is the error mean square. If the null hypothesis, Ho, is true then the statistic follows the F distribution with K degrees of freedom in the numerator and {n- (K+1)} degrees of freedom in the denominator.
Hence, to sum up all, an F test is basically an overall significance test for the calculated regression equation.
Ignoring Ho means that the null hypothesis is incorrect or we accept Ha i.e. all the parameters are not equal. Moreover, all the independent variable’s slopes are also unique from each other. It is also concluded that there exists an important relationship between the six independent variables, dependent variable y and corporation profits.
Just as the t-test for the individual diverse variables, the test on individual regression coefficients was also carried as t-test. The importance of t-test is basically for individual regression coefficients in the multiple linear regression models. When a significant variable is added to a regression model, it makes it more effective while on the other hand, adding a less significant variable makes the model worse. Following are the hypothesis statements for testing the importance of a unique regression coefficient, also known as Bi:
Hypothesis Test:
H0:Bi=0where Ha: Bi is not equal to 0
Test statistics:
T= bi/Sbi
Where, bi is the slope or the ratio of the changes in Y and changes in Xi.
If the p value is less than alpha, Ho is ignored.
The basic significance of a T test is to conduct it individually with all the independent variables to find out the significance of each variable to the variability of Y. Here, through the t-test, we draw significance of population in outdrawing the variability in the corporation profits. With ignoring or rejecting Ho, it means that the null hypothesis is not correct or Ha is accepted. In other words, Bi is not equal to zero and Xi is a statistically important variable.
Conclusion:
Future research: Forecasting- Trend projection method:
The last statistical technique of the project is Trend projection with which we can predict the Corporation profits for next three years. The forecasting method is called “Linear Trend Regression”. One modification has to be with the Y data as the numbers are very big, so we will keep them in 10000 units. The trend projection method clearly suggests that there will be a hike in the corporation profits in the near future. The calculated equation for the trend depicts a positive slope so as to supplement the projected corporation profits in the next few years. Due to this, the figures have been increasing since last few times. The industry has been earning huge profits in most countries in the world and this is why the estimated figures in the above methodologies seem to be nearly correct.
References:
- Energy Information Administration. “Energy Overview .” Annual Energy Review. Table 1.1. 2005. 1 June 2007 http://www.eia.doe.gov/emeu/aer/pdf/pages/sec1_5.pdf>.
- Ibid. Total consumption is 99.89 Quadrillion Btu, Fossil Fuel Consumption is 85.96 Quadrillion Btu. Percent from fossil fuel is 85.96/99.89 = 86%
- Inventory of U.S. Greenhouse Gas and Sinks: 1990-2005. “USEP A #430-R-07-002, Table 2-16: U.S. Greenhouse Gas Emissions by Economic Sector and Gas with Electricity-Related Emissions.”. April 2007. 14 June 2007
- World Resources Institute. “Climate Analysis Indicators Tool (CAIT).” 2007. 14 June 2007 http://cait.wri.org/cait.php?page=yearly>. U.S. is listed at 5,912 for 2004, while the world is listed at 27,043. Percentage for U.S.: 5,912/27,043 = 21.86%.
5. U.S. Census Bureau. “U.S. and World Population Clocks – POPClocks.” 22 November 2006. 25 May 2007
6. IPCC, 2007: Climate Change 2007: The Physical Science Basis. Contribution of Working Group III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Summary for Policymakers, section B.
7. IPCC, 2007: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. FAQ 3.1.
Appendicices
