Income and Expenditure
Introduction
Income and expenditure contributes largely to economic measures of an individual, country or continent. They determine the credit worthiness of a person or economic stability of a given country. Hence, my report will cover how income of an employee relates with his expenditure in the U.S. What actually am determined to prove is that, when a person gets higher income will his or her expenditure increase or decrease? For instance, I managed to find discrete data concerning income and expenditure from the ‘Economic data for the U.S.: http://www.bea.gov/’. The data had three variables namely, months starting from the month of April 2013 to march 2015, income per each month represented in $1000 and expenditure each month in $ 1000. Regarding the same, my research question is, how the increase of income affect expenditure. This set me to come up with a null hypothesis represented by Ho, stating that, income is directly proportional to expenditure against an alternative one which is, increase of income does not have any effect on expenditure. I will analyze my data using two-sample t-test in order to find out which of the set hypotheses is true and which one is false.
Exploration of the Data Collected
Income and expenditure data in the U.S had some errors which might cause problems during the analysis process. To make sure data was pure and ready for the same, I used STATA program to measure the extent of cleanness and purity in the data content. Then, on the readily available data, I applied both Minitab program and excel to present it using graphs, scatter plots, time series and carrying tests to ascertain the meaningfulness in it.
For any analysis part, regression is meaningful, as it leads to some assumptions which when proved and analyzed keenly, can be right. I did this in four ways namely
Linear relationship. The increase of one variable can cause a corresponding increase on the other. This actually shows direct proportionality. For instance in my data, the increase of income causes an increase in expenditure hence have a direct association. A line plot displayed below shows the relationship between income and expenditure.
In the above line plot, there is a direct link proportion between income and expenditure. When an individual’s income increases, his expenditure rate also increases. This is because of the need to make life meaningful by looking on ways to satisfy human wants.to some extent this is well described by the need to stay comfortably which leads to the increase of expenditures.
Regression Analysis: Income versus expenditure
When I used the Minitab, the output was as shown below concerning linear regression.
The regression equation is
Income = 0.093 + 1.169 expenditure
S = 13.9933 R-Sq = 100.0% R-Sq(adj) = 100.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 94671025 94671025 483475.22 0.000
Error 23 4504 196
Total 24 94675529
With the same explanation, there is a perfect direct relationship between income and expenditure. This is evidenced by the output displayed above. With the help of a linear equation model, I came up with the fitted line plot. The correlation coefficient was 1 meaning the strength of the relationship was purely perfect.
Normal distribution. This is exhibited when histograms of residuals for each linear regression line are drawn. The bell shapes displayed by histograms show the normality of data distribution. The plot below shows normal distribution.
The plots are close together and in a straight line. The evidence is a sample showing normal distribution feature. Hence income being a variable in our data set, is normally distributed.
Standard deviation. It is shown by drawing a scatter plot of residuals against a dependent variable like expenditure. If there is any pattern which shows some deviations or outlaws then our data will be questionable. The plot bellows displays residuals on expenditure.
Regarding on the output plot above, there points plotted are scattered all over in some pattern, kind of zigzag. The points do not show any linearity. One is unable to make a conclusion on the same. The output above, represents deviations from the normal way of distribution thus displaying outliers. It’s difficult for further analysis to be done on expenditure due to the presence of outliers.
The regression summary is as displayed below
The above display has some symbols which stands for some credentials. For example, ns which means number of observations made, x variable which stands for expenditure and Y which is for income.
Analysis
The analysis part includes both graphs and statistical tests carried out on the data. The range of graphs used are histograms, time series plots and pie charts. The summary statistics and the descriptive statistics has also been shown. The test appropriate for this type of data is t-test which assumes equal variance of the variables to be tested.
Concerning the two statistical descriptive summary done above, income mean tends to be more than expenditure mean. This simply shows that an individual earns more than he actually spends. This is a good plan, since there is something small left for savings. But if it happens that, the expenditure mean is greater than income mean, then there is evidence of poor planning. The law of economics states that, income should be more than what actually an individual earns. Confidence levels also differ by a large margin. Income confidence level is about 14.81952826 while that of expenditure is 7.63260404. This too acts as an evidence for income being more than expenditure.
The histograms showing how income and expenditure relate are drawn below, each variable on its own.
The income histogram above shows that, there is some skewness. In the first look, am able to generalize what is being represented here. The higher frequency of individuals earn less than $2,000,000. Very few people who earn a lot to sustain themselves in life.
Expenditure in the same case, has some collinearity in between its values and the error term. That’s is why we experience the abnormality rise of bars in the histogram. The amount spend during the given period in expenditure is less than $200,000 while very few individuals who spend a lot in life matters.
The two time series plot almost have a similar look but they are quite different. This is seen on the accuracy measures. The income time series has the following accuracy measures, MAPE=8, MAD=413. MSD=3913728. While expenditure time series has MAPE of =6. MAD=348, MSD=2871986
The pie charts also gave a well analyzed data, whereby each slot or portion represented information carried by data. They are as displayed below
The t-test carried out shows that, the t-statistic is greater than the t-critical. That is, t-stat > t-critical. 7.766449 >2.012896. Hence, this will lead me to make generalizations on the set hypothesis.
Conclusion
Basing my arguments on the t-test carried out, I had to make a decision concerning the set hypotheses explained in the introduction. Since the t-stat is greater than the t-critical we accept the null hypothesis which says that income is directly proportional to expenditure. As analyzed above, many instances shows a linear relationship between income and expenditure. This actually means that, as an individual’s income increases, definitely his expenditure increase. This follows the fact that, one tries to satisfy the numerous human wants to gain comfortability. The desire to make hefty steps in order to get a better living standards, an individual can spend to find ways on getting opportunities which will bring profit back.
As part of the U.S governmental concern, an employee’s salary together with allowances, is what we refer to income. Every employee regardless of the type of job opportunity, gets a standard income. This contributes to a well-balanced economy which out competes many countries. The U.S government has well planned strategies of job evaluation processes. Moreover, they have awesome ways in dealing with companies and other private money making institutions to at least balance and bring into order every strategy leading to a stabilized economy.
References
Stone, R., & Stone, G. S. (1962). National income and expenditure. Chicago: Quadrangle Books.
Great Britain. (1791). Report from the select committee appointed to examine and state the several accounts: And other papers, presented to the house of commons in this session of Parliament, Relating to the Public Income and Expenditure ; and To report to the House what has been the whole Amount of the Public Income and Expenditure during the last five years, and what may be expected to be the Annual Amount in future ; and also, What Alteration has taken Place in the Amount of the Public Debt. since the 5th of January, 1786. Ordered to be printed May 10, 1791. London: Printed for J. Debrett opposite Burlington-House, Piccadilly [by T. Burton
Great Britain., & Great Britain. (1951). National income and expenditure. London: H.M.S.O.
Canada., Statistics Canada., Statistics Canada., Statistics Canada., Canada., & Statistics Canada. (1969). National income and expenditure accounts. Ottawa: Dominion Bureau of Statistics
