Quantitative procedures are strategies that bring insight into decision making through systematic and powerful study of quantitative data. 2011 (Vineethan). The empirical paradigm is a phenomena in which data is utilized to assume cause and effect linkages; it has a substantial impact on quantitative studies. Thus, quantitative procedures are founded on empirical observations and critical analysis of results (Learning, n.d.). The emphasis of this study is on data analysis, presentation, and interpretation of graphical, correlation, and regression analysis. The use of diagrams and graphs to analyze economic issues is referred to as graphical one. Such graphs and diagrams include bar charts, Pareto diagrams, line graphs, scatter plots, etc. On the other hand, correlation analysis tries to determine and quantify the existence, magnitude, and direction of the linear relationship between two or more variables. Regression analysis will help estimate the existence of a relationship between a dependent and independent variable(s). It is important to comprehend that correlation and regression analysis have some assumptions, which must hold for effective analysis. Besides, the selection of the best analysis method, graph, and critical interpretation are the key objectives of this paper. This assignment seeks to test how to inculcate skills and knowledge in quantitative business research, mitigation of availed information, and application of statistical tools in data analysis. This study will use Microsoft Excel for analysis. Typically, data analysis and presentation help identify usable and useful information. Therefore, it summarizes and describes data, identify relationships between variables, identify differences between variables, and forecast outcome. Also, decision making on which data analysis method to use, which graphic presentation or data to display is based on scales of measurement namely nominal, ordinal, interval, and ratio. Therefore, understanding the type of scale is critical in data analysis.
Task 1 Graph (Descriptive statistics)
Graphical representation provides a quick way of viewing and assessing trends of data. Graphical presentation works hand in hand with a descriptive statistic to postulate the desired results. Descriptive statistics can be defined as a descriptive coefficient that summarizes a given sample or population. It is further categorized into measures of variability and central tendency/spread. A measure of central tendency/spread identifies a central position in a set of data to describe it by use of a single value. These measures are mean, mode, and medium; their appropriateness vary under different conditions. A measure of variability describes the amount of spread in a set of data. The frequently used measures of spread are the range, interquartile, variance, and standard deviation. It is worth noting that all descriptive statistics are either measure of variability or central tendency. Whereas statistic and data analysis result into tabular and or numeric output, graphical techniques present such data in pictorial forms. Graphical analysis can be described as the study of interdependent occurrences by analysis of graphical presentations (TheFreeDictionary, n.d.). Such graphs include bar graphs, line graphs, charts, Pareto diagrams, etc. The integration of graphical analysis and descriptive statistics enhances visualization of data. Descriptive statistic and graphical analysis involves organization of data, differentiate data display tools, recognition of measures of central tendency and finally a comparison of measures of variability. Graphs are mainly important, as they provide data insight to analysts (facilitate assumption testing, selecting and validating models) and help illustrate important concept during the presentation. Exploratory Data Analysis is highly depended on these pictorial techniques. Also, statistical graphics assist in determining outliers and relationships in a data set.
Graphical analysis has four objectives:
To explore dataset content
Find structure in data
Identify assumptions in statistical models
Communicate results
Also, the selection of relevant statistical graphics provides a mean of communicating the central message that is present in the data to others. Graphs can be used to analyze a single variable or to compare few data sets at time. For the task I, the graphical analysis that compares two data sets provided will be adopted.
Figure 1.
A comparative line graph helps to postulate the trend of values of different categories. The graph indicates that as years of post-16 education increases, the income level increases as well. This shows that there is a similarity between the two datasets. For instance, a person with nine years of post-16 will earn more than that one with 4-year experience.
Figure 2.
The histogram is skewed to the right. This indicates from the surveyed people, a large percent earned between 9-21 £ ‘000 s. This may be attributed to fewer years of experience. The higher earners possess more experience than the rest.
The pattern postulated by this graph indicates that as the years of post-16 education increases, the income level increases at almost the same rate. This is a clear indication that income level is dependent on years of post-16 education.
Task 2: Correlation Analysis
Correlation coefficient analysis involves the study seeking to compare two or more variables and measuring their degree of their relationship. It is a fraction of the covariance between the two variables divided by their individual standard variations. This coefficient constant runs between -1 to 1. When the correlation coefficient is 0, it shows that there exists no relationship between the two variables. When the coefficient is greater than zero, it confirms that there is a direct proportionality between the parameters i.e. a rise in one parameter will lead to a corresponding increase in the other related parameter. When the coefficient is negative, it shows that the two parameters are inversely proportional. The more the fraction is towards one, the stronger the correlation and vice versa. For this method to be used successfully, one must hold the independent variable constant while the other variable is allowed to change. This relationship when represented graphically portrays a straight-line graph having the independent parameter on the X-axis and the corresponding dependent parameter on the Y-axis. For equal proportionality, the correlation coefficient is at 0.5. Deviations run at this point. It is an efficient method of assessing the costs in production units with their impacts in the organization. I have thus used this method in my study of a company that wishes to consider income level as a basis for building a model. This analysis seeks to assess the strength of the relationship between income level, some previous jobs done and the years of experience.
Correlation Matrix
Table 1.
Following the analysis, there exists a strong positive correlation of about 0.805 between the years of experience and the income earned by different employees. People with the higher number of years of experience made more money compared to those with low years of experience. Companies willing to hire highly experienced workers should be able to set a substantial amount of money to pay them. This is the fact that the employees with high skills are highly productive within the organization. It is efficient to work with experienced workers, as they require minimum training costs. They also do the job on time avoiding wastage of materials and deliver substantial output within the set deadlines. Skilled workers also save machine breakages, as they are familiar and at ease with their tools of work. This makes them be preferred at such high costs since they are cheap in the long run compared to the inexperienced workers who would make the companies incur more costs to make them competent.
The number of previous jobs done by the employees also affected the income they earned. This relationship reflected a correlation of 0.387. This correlation implies that the employees with more number of jobs done previously had corresponding higher income. These changes may have appeared due to the fact that when employees are not contented with their salaries within the organization, they utilize any chance of working with other agencies that provide better salaries.
The relationship between the years of work done and the years of experience indicated a strong correlation coefficient of about 0.452. The more an employee work in many organizations, the more he/she gains regarding working experience. Different companies have variable methods of production that they impart to their employees for efficiency. Woirkers, therefore, acquire vast knowledge, which they may sell off to other companies; this knowledge is, therefore, attributed to the experience provided within a similar production unit. These skills make them more marketable, as the organizations try to maintain them to stabilize their economies. This competition makes their current organizations to increase their salaries and hence their high wages.
TASK 3: Regression Analysis
Regression analysis consists of techniques used to model the relationship between a predicted variable with one or more predicting variable where the explained variable is modeled as a function of explanatory variables, regression coefficient, and the error term. According to Statgraphic Centurion, Regression can be categorized differently. This different types of regression model include simple regression, polynomial, non-linear, multiple and ridge regression. For the purpose of this paper, linear regression will be explored.
Regression can either be a representation of dependence, i.e. conditional expectations and condition distribution, or dependence of random variables. Linear regression employs a square method. When an explanatory regression power is higher enough to reflect the existence of relationship adequately, the model can be used to predict other variables, help identify relevant variables as well as establishing desired causal relationship between the dependent and independent variables (Yan and Gang, n.d.). This is postulated by the fitness of the model and existence of a linear relationship.
For regression to be effective, data is gathered, assembled, edited, transformed, and classified as variables of interest. The regression model is then employed to estimate the quantitative causal effect of the explained to explanatory variables. This typically entails assessing the statistical significance of the estimated relationship. Statistical significance implies that results from the experiment are attributed to specific causes rather than occurring by chance or randomly (Staff, 2017). Yan and Gang (n.d.) describe statistical significance as the degree of confidence of the how linear relationship is close to estimated statistical relationship.
Regression heavily relies on underlying some assumptions. These five key assumptions are:
Linear relationship- the relationship between the response and independent variables must be linear. This indicates that regression analysis is sensitive to outliers and can be demonstrated by use of scatter plot.
Multivariate normality. Variables are assumed to be normally distributed. It can be tested using Q-Q plots and Histogram
No or little multicollinearity. Assumes that Independent variables are not highly correlated with each other. Tested using Tolerance, correlation matrix, and condition index
No auto-correlation. The residual should have no correlation with each other and is tested using scatterplots
Homoscedasticity. Assumes that the error terms along the regression are equal. (Statistics Solutions, 2017)
Regression analysis has been criticized due to the application of assumptions which do not hold.
Interpretation of Results
Note: Regression statistics gives the ‘goodness of fit” measures. It tries to show how the linear regression calculated fits the data.
The correlation coefficient (Multiple R) demonstrates the strength of the linear relationship, i.e. 1 represents a perfect positive correlation relationship, 0.5 moderate, and zero NO relationship.
The Coefficient of Determination (R squared). It shows the number of points falling on the regression line.
Adjusted R square. Indicated the R-square is adjusted for the number of predictors in a model. Help predict the accuracy of coefficient estimates. Adjusted R square is applicable when there are more than one dependent variables.
Standard Error of the Regression: The standard error of the regression indicates on average how wrong the regression model is. The accuracy of prediction of the resulting regression model
Observations. This is the frequency/number of observations in a dataset (sample data).
Regression output
a. Co-efficient of multiple correlations. There exists a strong positive linear relationship between the variables this is evidenced by a high Multiple R of (0.90) hence signifying strong linear relationship.
The explanatory power of the results. R Square is at 0.82 indicating a strong fit for the explanation. This is because 82% of the changes in the income level are as a result of years of work experience, some previous jobs, and years of post-16 education hence higher goodness fit.
EXPECTED MODEL; multiple linear regression taking form;
Y=β0+β1X1+β2X2+β3X3+е
Resulting Model helps determine the impact of a change in one parameter on the income level. The resulting model of the study is;
Y=3.30+0.1.4X1+0.57X2+1.64X3
Note;
Y represents income level, X1 rep year of work experience, X2 rep number of previous jobs, and X3 rep years of post-16 education.
Statistical significance of the resulting model
The F-value is 13.31; it is higher than 2.5 hence the resulting model is statistically significant
Else; the significance F is 1.17 x10-3 therefore
Level of model significance= (1- 1.17 x10-3) x100=99.99% therefore the model is highly significant.
Intercept. The intercept indicates the significance of other factors does not consider in the study. The intercept is 3.30 which is greater than 1.96 hence it is significant. Other factors not considered in the analysis have the significant effect of the changes in income level.
Among the explanatory variables examined, year of post-16 education has the highest T statistics (2.85) indicating the highest level of significance while some previous jobs are the least significance with a T statistic of 0.53. This suggests that year of post-16 education has a great impact on the level of income.
Conclusion
Businesses are shifting their attention to management and mitigation of data as a tool of competitive advantage. This necessitates possession of data collection, transformation, analysis, and interpretation skills to facilitate business decision making. Quantitative Techniques in business has become a focal tool in decision making in organizations.
Quantitative techniques in business as a course seek to instill analytical skills that will be vital for such analysis. To comprehend data analysis and interpretation, it is crucial to have basic knowledge on data types, either qualitative or quantitative in nature. Besides, it is very necessary to understand the scales of measurement, including nominal, ordinal, ratio and interval scale, for easier understanding of data and selection of analysis method.
Data analysis starts with the identification of data manipulation and finally mitigation through analysis aiming to achieve useful skills in the quantitative techniques theoretical understanding of necessary analysis method. The analysis method is dependent on the type of data and the purpose of information obtained. Regression analysis tries to establish the existence of relationships between the dependent variable and two or more independent. Regression analysis is guided by some assumption which must hold for the analysis to be varied. These assumptions include linearity, homoscedasticity, no auto-correlation, etc. On the other hand, correlation analysis explores the nature and degree of relationship between two or more variables. Pictorial presentation has increasingly become important in data analysis. They help determine the trend, pattern and or relationship between various categories. The findings of the analysis indicate that there existed a strong relationship between income level and the independent variable. The explanatory power and goodness of fit of regression analysis were way high. This indicates that years of experience, years of post-16 education profoundly impact the income level of employees. Some the previous jobs have no strong influence on income levels. Working with a variety of organizations leads to greater experience and this experience, in turn, makes the employees demand high salaries. The companies, on the other hand, are willing to pay the high wages as they are assured of increased productivity that leads to higher profits which are the main aim for all organizations. It is, therefore, an obligation of the companies to pay their workers fairly if they want to retain the experienced workers. Otherwise, they may be taken away by the well-paying competitors who are a threat to their economy. They should make plans to review their salaries with the trends in other companies. This is the realization that as time goes on, their workers are gaining more experience, and their value is appreciating too Managements should devise new ways of retaining employees for sustainable growth. They should employ data intelligence to facilitate decision making for competitive advantage in the market.
References
Crossman, A., 2016. Correlation - definition in the study of sociology. [online] Available at: http://sociology.about.com/od/C_Index/g/Correlation.htm. [Accessed 26 Feb. 2017].
Learning, I. (n.d.). Theory and quantitative methodology. [online] Available at: http://libweb.surrey.ac.uk/library/skills/Introduction%20to%20Research%20and%20Managing%20Information%20Leicester/page_44.htm [Accessed 26 Feb. 2017].
No author identified. (n.d.). Data Analysis, Interpretation, and Presentation. Available at: http://www.uio.no/studier/emner/matnat/ifi/INF4260/h10/undervisningsmateriale/DataAnalysis.pdf. [Accessed 26 Feb. 2017].
Statistics Solutions, 2017. Assumptions of linear regression - statistics solutions. [online] Available at: http://www.statisticssolutions.com/assumptions-of-linear-regression/ [Accessed 26 Feb. 2017].
Staff, I. (2017). Statistical significance. [online] Available at: http://www.investopedia.com/terms/s/statistical-significance.asp [Accessed 26 Feb. 2017].
TheFreeDictionary.com. (n.d.). Graphical analysis. [online] Available at: http://encyclopedia2.thefreedictionary.com/graphical+analysis [Accessed 26 Feb. 2017].
Vineethan, S., 2011. Quantitative techniques for business. Available at: http://www.universityofcalicut.info/SDE/Quantitative_Techniq_Business_on25Feb2016.pdf [Accessed 26 Feb. 2017].
Yan, X., and Gang Su, X. (n.d.). Linear regression analysis theory and computing. [online] Available at: http://www.manalhelal.com/Books/geo/LinearRegressionAnalysisTheoryandComputing.pdf [Accessed 26 Feb. 2017].
