Good Research Paper On Problem Statement
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The use of energy is the basis of human society and allows him to modify the environment. Social forms of energy are crucial for the reproduction of the results. In the industrial and post-industrial societies, the development of energy resources needed for agriculture, transport, waste management, development of information technology and telecommunications and other sectors of the economy, the development of which is to achieve a high level of social development. On the other hand, the spontaneous growth of energy consumption as a result of the industrial revolution and the post-industrial revolution led to a variety of serious problems, some of which (e.g., global warming) pose a great threat to mankind.
When it comes to society, the word energy is used as a synonym for energy resources and most often refers to concepts such as fuel, oil products and electricity. This is a useful source of energy, i.e. they can easily be converted into other forms of energy that are useful for specific tasks. This difference of the concept of energy in the physical sense can sometimes cause confusion because energy resources are not stored like energy physics. The actual energy content does not change, but when it is transformed, for example, in the heat, it becomes less useful to society, and it is said that the energy has been used.
When using phrases such as "energy crisis" and "need to save energy," it should be primarily borne in mind that the energy used in human society, mainly in accordance with the nature of its existing forms of social development, i.e. it does not is the law of conservation of energy as it is formulated in physics. In order to save social energy must first optimize the nature of social development. Energy production and consumption are inextricably linked with the global economy. To carry out any economic activity requires energy: the production of goods, transportation, power for computers and other equipment. Economic growth is always associated with an increase in productivity, and increase productivity, as a rule, using the new automated production, which is required for this form of energy like electricity.
Many researchers see the inextricable link of production growth with an increase in power consumption. However, this relationship is not unbreakable. Many governments are considering increasing energy efficiency, and thus reducing dependence on energy as an important direction of economic policy.
In this paper we will show the basic concepts of statistical analysis related to a real world economic problem. We are interested how the United States prices of the energy resources are related. To investigate this problem the historical data of the gasoline and electricity prices has been found on the period from 1979 to 1996.
Also, we are interested how these prices are associated with the minimum wage value during the same period of time. The minimum wage is officially set by the state minimum wage in the enterprises any form of ownership in the form of lower monthly rate or hourly rate. The value of the minimum wage is not always tied to the subsistence minimum. It is determined in each period financial capabilities of the state, changes periodically (nominally always increases). Denomination minimum fee is used to calculate the size of government taxes, fees and fines. The minimum wage is tied and the amount of income tax on individuals.
The data is collected from http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html (Price of Electricity, Price of Gasoline, Minimum Wage). Based on these three data sets we calculated the average yearly indicators for each variable. The table below represents the data by year:
We begin with a descriptive statistics. It helps us to understand the basic characteristics of the variables distribution. Descriptive statistics allows summarizing the initial results obtained by observation or experiment. Procedures are reduced to the grouping of data on their values, the construction of the distribution of their frequencies, identification of central tendency of the distribution (e.g., arithmetic mean), and finally to the estimation variance of the data in relation to the central tendency found. Descriptive statistics provides new information, quickly understand and evaluate it thoroughly, i.e. performs the function of a scientific description of the research subjects, and this justifies the name of methods of descriptive statistics howling designed to make a set of individual empirical data on the system for the visual perception of shapes and numbers: frequency distribution; indicators of trends, variability and communications. These methods are calculated statistics of random sampling, which serve as the basis for statistical inference.
I use Minitab 16 Statistical Software to perform all statistical calculations in this paper
Descriptive Statistics: Average yearly price of ; Average yearly price of
Variable N N* Mean SE Mean StDev Variance Minimum
Average yearly price of 18 0 40,91 1,53 6,49 42,10 25,33
Average yearly price of 18 0 1,1311 0,0319 0,1353 0,0183 0,9000
Variable Q1 Median Q3 Maximum Range IQR
Average yearly price of 38,02 40,91 46,37 49,30 23,97 8,35
Average yearly price of 1,0025 1,1450 1,2325 1,3800 0,4800 0,2300
Variable Mode Mode Skewness Kurtosis
Average yearly price of * 0 -0,83 0,75
Average yearly price of 0,95; 1,11 2 -0,23 -0,62
The best way to understand the distribution of the data is to plot it on a graph. We construct frequency histograms to see how the data is distributed. The bell-shaped blue curve on each graph represents a normal distribution (Gaussian) curve.
We can see that the distributions of the variables are not so close to the normal curve. That’s why this may bias the further procedures of our research.
The next step of our analysis is to check whether prices of gasoline, electricity and minimum wage are associated or not. For this purpose we use correlation analysis. The main objective of the correlation analysis is to identify the closeness of the connection between the random-ranks by evaluating the correlation coefficients. Correlation analysis is to test hypotheses about the relationships between variables using correlation coefficients. The correlation coefficient is a two-dimensional descriptive statistics, quantitative measure of the relationship (the joint variability) of two variables. Thus, correlation analysis is a set of methods for detection of correlation between random variables or attributes.
It seems that the minimum wage and price of electricity are linearly associated, the other two plots shows many outliers – the points are not grouped as a trend line.
Correlations: Price of electri; Price of gasolin; Minimum wage adjus
Price of electri Price of gasolin
Price of gasolin 0,016
Minimum wage adj -0,832 0,314
Cell Contents: Pearson correlation
If we set the level of significance alpha at the most common level of 0.05, we can conclude the following:
Since p-value of the correlation coefficient between the average yearly prices of electricity and gasoline is 0.948, it is insignificant. We can’t conclude that the prices are associated linearly.
Since p-value of the correlation coefficient between minimum wage and price of gasoline is 0.205, we also say that it is insignificant and there is no linear dependence here.
However, the p-value of the correlation between minimum wage and price of electricity is lesser than 0.001. This is an evidence of a significant linear relationship. As the correlation coefficient is -0.832, the association is strong and negative.
The next step of this research is to develop a linear regression model to make forecasts. It will be meaningful only for two variables: Price of electricity and minimum wage, because we know that price of gasoline is not associated with these two variables.
We believe that as the overall wage increases, it also affect the wages of employees working in electricity sector of the national economy. And this involves to increasing of the electricity production cost, hence, the prices are growing. That’s why the price of electricity is a response variable and the minimum wage is a predictor.
Regression Analysis: Price of electri versus Minimum wage adjus
The regression equation is
Price of electri = 92,4 - 8,83 Minimum wage adjus
Predictor Coef SE Coef T P
Constant 92,424 8,642 10,69 0,000
Minimum wage adjus -8,834 1,474 -5,99 0,000
S = 3,71326 R-Sq = 69,2% R-Sq(adj) = 67,2%
Analysis of Variance
Source DF SS MS F P
Regression 1 495,05 495,05 35,90 0,000
Residual Error 16 220,61 13,79
Total 17 715,67
According to the regression analysis, we have obtained that price of electricity and minimum wage are related in the following way:
Price of electricity=92.4-8.83*Minimum wage
According to ANOVA output, the model is significant (F=35.9, p<0.001). The coefficients of the regression equation are also significant (p<0.001). The coefficient of determination is 69.2% and it shows the approximate percent of variation of the response variable which is explained by this model.
In this research we have concluded that the prices of gasoline and electricity are not related. However, there is a strong linear negative association between minimum wage and prices of electricity. The developed linear regression model is significant and is good for using. However, it shouldn’t be used for far forecasts because the various economic factors may affect price of electricity. The model may be improved if we add some factors to develop a multiple regression model, but the addition of the factors must be evidence-based and well-grounded.
William H. Kruskal and Judith M. Tanur, ed. (1978), "Linear Hypotheses," International Encyclopedia of Statistics. Free Press, v. 1,
Birkes, David and Dodge, Y., Alternative Methods of Regression. ISBN 0-471-56881-3
Lindley, D.V. (1987). "Regression and correlation analysis," New Palgrave: A Dictionary of Economics, v. 4, pp. 120–23.
T. Strutz: Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond). Vieweg+Teubner, ISBN 978-3-8348-1022-9.
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