Quantitative Technics in Business - Assignment Example

Task Graphs Graph Graph showing ROCE RSF against RTA X axis scaling unit year; Y axis scaling unit = 5% Interpretation: The above graph shows the scatter diagram of years along with X axis vs. RSF(%), ROCE(%) and RTA (%) as variables given along with Y axis. The scatter diagram shows that there exists a positive correlation between ROCE and RTA and also between RSF and RTA. The RTA values remain almost the same through out the 10 years whereas the RSF values show a downward trend except for the years 2006 and 2013 whereas the RTA shows both upward and downward trends over the last 10 years of operation. Graph 2: Graph showing ROCE (%) against LQR (X) X axis scaling: 1 unit=0.1; Y axis scaling: 1 unit = 2% Interpretation: The above graph shows the scatter diagram of years in X axis and LQR & ROCE (%) in Y axis. The scatter diagram shows that there exists a positive correlation between ROCE and LQR. The LQR is almost stable throughout 10 years whereas ROCE started with high value depreciated steeply in the next two years 2005, 2006 and started again with a high jump in 2007 and shows downward and upward trend after wards. The LQR values are consistent over the last 10 years whereas the ROCE varies much over the 10 years, showing both upward and downward trends. Graph 3: Graph showing PAIT (Y axis) against Tax (£’ Millions) (X axis) X axis scaling: Y axis scaling: 1 unit = 1000 Interpretation: The above graph shows the scatter diagram with years in X axis and the variables TAX & PAIT in Y axis. A comparison of TAX and PAIT shows that there exists a positive correlation between TAX & PAIT except the period from 2010 to 2011. The tax is showing both upward and downward trends but did not vary much whereas the PAIT is showing a high variation during the year 2012. Graph 4: Graph showing PAIT (Y axis) against Admin. Expenses (£’ Millions) (X axis) X axis scaling in years; Y axis scaling: 1 unit = 5000 units Interpretation: The above graph shows the scatter diagram of years in X axis and ADMIN. EXP and PAIT in Y axis. This also ensures that there exists a positive correlation between PAIT and ADMIN EXP. The ADMIN EXP shows almost increasing trend except for the years 2010 and 2011. PAIT showing less variation compared to ADMIN EXP. Task 2: Correlation Analysis Table 2: Table showing the correlation coefficients   RSF(%) ROCE(%) RTA(%) RSF(%) 1 ROCE(%) 0.308 1 RTA(%) 0.919 0.488 1 Analysis: The correlation coefficient founded by Karl Pearson depicts the relationship between two random variables especially two continuous random variables. The formula for the correlation coefficient is given by the formula where the term, is the covariance term and the term which is the joint variation of the variables taken from their respective means, the term is the standard deviation of x and the term is the standard deviation of y. The range of Karl Pearson’s correlation coefficient is from -1 to +1. If the correlation coefficient is nearing to -1, it denotes a strong negative relation between the two variables x and y (if one increases the other decreases and vice versa), and on the other hand, if the correlation coefficient is nearing to +1, it denotes positive strong relation between the two variables x and y (if one increases the other also increases and if one decreases other also decreases) (Curwin and Slater 2007). If the correlation is nearer some where around 0 from either directions (positive or negative), it indicates weak and almost nil correlation between the two variables. To find out the existence of any type of correlation roughly, we take the help of scatter diagram (Lucey 2002). We use Microsoft Excel’s Data Analysis pack to obtain the correlation coefficient matrix. The correlation coefficient is tested through the test of significance procedure that under null hypothesis, H0: The correlation coefficient is not significant against the alternative hypothesis H1: The correlation coefficient is significant. The formula for testing the correlation coefficient is given by Student’s t-test using the following expression: to =  with (n-2) degrees of freedom where n is the sample size. If the correlation coefficient is significant, we conclude that the relationship between the two given variables is highly significant and influential otherwise we say that the correlation coefficient is not significant. Table 3: Table showing the significance of correlation coefficients at 5% level of significance Variables Correlation coefficient df t-statistic t-table value Prob. RSF & ROCE 0.308 8 0.916 2.306 0.387 RSF & RTA 0.919 8 6.593 2.306 0.000 ROCE & RTA 0.488 8 1.581 2.306 0.152 Interpretation: The correlation coefficient between RSF and ROCE is positive but weak since the probability of significance being 0.387 (>0.05) and it is also emphasized by comparing the t statistic (0.916) being less than the t-table value (2.306) for 8 d.f. at 5% level of significance which concludes that there exists a positive correlation between RSF and RTA, but it is not significant. In this case, the null hypothesis H0 is accepted and the correlation coefficient between RSF and RTA is not significant. The correlation coefficient between RSF and ROCE is highly positive and strong and significant since the probability of significance being 0.000 (0.05) and it is also emphasized by comparing the t statistic (1.581) being less than the t-table value (2.306) for 8 d.f. at 5% level of significance which concludes that there exists a positive correlation between ROCE and RTA, but it is not significant. In this case the null hypothesis H0 is accepted and the correlation coefficient between ROCE and RTA is not significant (Wisniewski 2010). From all the above paragraphs concerning the correlation coefficients between three variables, the only significant correlation coefficient is between RSF & RTA with r=0.919 for 8 d.f. at 5% level of significance since the observed value (test statistic)of 6.593 is greater than the expected value of 2.306 with probability of significance being 0.000. Therefore, the increase (decrease) in RTA is accompanied with the increase (decrease) in RTA but not to that extent since the correlation is weak. Strength of relationship The strength of relationship between RSF and RTA is very high with 0.919 followed by the relationship between ROCE and RTA with 0.488 and finally the relationship between RSF & ROCE is the lowest with 0.308. But all of the relationships are positive and from table 1 only the relationship between RSF and RTA is highly significant. Other correlations are not significant. Task 3: Regression Analysis Table 4: Table showing the multiple R, R square Multiple R 0.549 R Square 0.301 Adjusted R Square 0.101 Standard Error 1833.595 Observations 10 Table 5: Table showing the significance of overall regression Source of variation df SS MSS F Significance F Regression 2 10129061.23 5064530.62 1.506 0.286 Residual 7 23534506.77 3362072.40 Total 9 33663568       Table 6: Table showing the individual regression coefficients Variables Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2285.821 2802.699 0.816 0.442 -4341.508 8913.151 ADMIN EXP(£’m) -0.073 0.103 -0.707 0.502 -0.316 0.171 TAX (£’m) 1.828 1.212 1.508 0.175 -1.039 4.694 Interpretation: Regression analysis is used to predict a dependent variable based on independent variable(s). The regression analysis done in MS Excel is by the method of least squares and the coefficients are unbiased since principle of least squares gives best unbiased estimates. Here our regression equation is given by y=a+b1x1+b2x2 where a stands for intercept in Y axis, x1 represents the independent variable admin expenses and x2 represents the independent variable admin exp whereas y represents the dependent variable PAIT (profit after interest and tax). Here the regression equation is PAIT = 2285.821 - 0.073 * ADMIN EXP+1.828 * TAX (from table 6). The regression equation is not significant since the probability of significance being 0.286 (>0.05). The explanatory variables ADMIN EXP and TAX are not able to predict the explained variable PAIT. So, further investigation is needed in this case. There may be possibility that if some more cases (sample size) are added, then better prediction can come out. But as of now, the regression coefficients are also not significant (refer table 5). The negative regression coefficient of -0.073 with probability of significance being 0.502 (> 0.05) indicates that admin expense have very minimal impact on PAIT and the positive regression coefficient of 1.828 indicates that there is a positive impact of tax on PAIT but very minimal since the regression coefficient is not significant (refer table 6) with probability of significance being 0.175 ( > 0.05). The intercept of 2285.821 also not significant with probability of significance being 0.442 ( > 0.05). Also from table 4, the R square being 0.301, only 30% of the dependent variable PAIT (explained variable) is explained through the independent variables (explanatory variables) administrative expenses and tax obligation which is very less for a sample size of 10, that is why the multiple correlation coefficient R showing non significance with probability of significance being above 0.05. The standard error of regression is also an important measure in the prediction equation (Sekaran 2006). It gives precise predictions since it gives better results than the R squared and much more reliable than the R squared statistics. R squared can be used in better precise predictions, when the R squared statistics shows a value above 0.8, then only the regression equation can be most precise, but with R squared value less than 0.8, the regression equation becomes less precise and forces the statistician to use either more sample size or include some more variables which is out of hand of the statistician. In the above regression table (table 6), the standard errors of the regression coefficients of intercept and admin exp being greater than the regression coefficients itself, it leaves a question about the regression equation and makes it unreliable for prediction purposes. But for the independent variable TAX, the standard error is less than the regression coefficient which can be used for prediction purposes despite it being non significant. However, to conclude, the independent variables ADMIN EXP and TAX are not to be used for predicting the dependent variable PAIT. Table 7: Table showing the observed PAIT, predicted PAIT & residuals vs. The independent variables ADMIN EXP & TAX Observation Observed Predicted PAIT (£’m) Residuals 1 (2004) 963 2954.126 -1991.12591 2 (2005) -723 1843.224 -2566.22383 3 (2006) 3616 4392.603 -776.60305 4 (2007) 4172 3601.694 570.305985 5 (2008) 3512 2221.673 1290.32656 6 (2009) 5249 2184.904 3064.09563 7 (2010) 5126 4634.551 491.449335 8 (2011) 5256 4650.705 605.295443 9 (2012) 3872 3934.525 -62.5246274 10 (2013) 3277 3901.996 -624.995532 The above residuals indicate that the residuals are far away from 0 in all the observations and much more investigations are needed for the regression analysis since the regression is not significant and the residuals are authenticated for the same and the independent variables should be preferably chosen for a significant regression, more explainable independent variables rather than ADMIN. EXP and TAX should be chosen for the dependent variable PAIT. Also it is noted to be that the residual for the year 2012 is the minimum in magnitude and the residual for 2009 is the maximum. Therefore there must be a huge policy change might have taken place during the year 2009-2012. Conclusion The present data set were collected for Barclays Bank for 10 years from 2004 to 2013 and the most important variables included are RSF (%) which refers to return on share holder’s funds, ROCE (%) which denotes Return on Capital Employed, RTA (%) which denotes Return on Total Assets, LQR (X) which denotes Liquidity Ratio, ADMIN EXP which denotes Administrative Expenses, PAIT (£’Millions) which denotes Profit After Interest and Tax, TAX (£’Millions)which denotes Taxation. At the outset there are seven variables analysed through descriptive statistics and it is given in table 1. The coefficient of variation is a measure of reliability and it is the lowest for ADMIN EXP (32.5%) and the highest for the variable ROCE (80%). The most important variables are correlated. Those variables are RSF, ROCE and RTA. Among the three correlations, the correlation between RSF and RTA is the highest with 0.919, therefore the variable return on shareholder’s funds is highly positively associated with the variable return on total assets. Also a regression equation was run through MS Excel with dependent variable being PAIT and the independent variables being ADMIN EXP and TAX obligation. The regression equation seemed to be less precise with both the regression coefficients being non significant and also the intercept adding to the non significance leaves the regression equation less precise and unreliable for future prediction purposes. This issue of unreliability for future prediction is a key issue. However there is an alternative to it. That is, an alternative can be either to increase the sample size or include more independent variables to make a significant impact on PAIT. So there must be some other variables / reasons behind the solely two independent variables ADMIN EXP and ROCE in prediction of PAIT. The data is collected for only 10 years, so the reliability is less. So, if the sample size is increased, it may lead to high reliability or another way of doing so is to include some more important variables which are a very good predictor for the dependent / explained variable PAIT. The financial ratios play a vital role in deciding a company’s growth and this is also a trend for the company’s profitability. So, once the financial ratios get regularized over a period of time, the business becomes stable and further one can estimate the profitability of the company easily. This way the company’s future growth can be formulated. The residuals between the observed and expected values will keep a minimum so that the future prediction of the dependent variable, based on future period and intermittent period, can be estimated easily. Among all variables, the most contributing variable towards the decision making is ADMIN EXP as it is having the least coefficient of variation. Much cannot be ascertained through the structure of the variables. The normality of the values also need to be checked, then proper transformation viz. log, arcsine transformation can be applied to know the relationship in a much better way. Inclusion of more reliable variables and deletion of highly unpredictable variables can result in a better regression equation hence much robust prediction. References Curwin, J and Slater, R., 2007. Quantitative Methods for Business Decisions, (5thedn) Chapman& Hall. Lucey, T., 2002. Quantitative Techniques, Thomson Learning Sekaran, U., 2006. Research Methods for Business: A Skill Building Approach. John Wiley & Sons. Wisniewski, M., 2010. Quantitative Methods for Decision Makers, (5th edn), FT Prentice Hall. Read More