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QuantitativeDecisionMaking.docx

Quantitative Analysis Quantitative Decision Making Eik Den Yeoh 2015 Contents 1.0 Introduction 2 2.0 Objective 3 2.1 Define Hypotheses 3 3.0 Finding and Discussion 4 3.1 Two Sample T-Test for Sample 4 3.2 Correlation and Multiple Linear Regression 5 3.3 Forecasting Techniques 7 4.0 Conclusions & Recommendations 9 5.0 Reference 10 6.0 Appendix 1.0 - VARIABLES 11 6.0 Appendix 2.0 - Data 11 6.0 Appendix 3.0 16 Document History and Version Control Name Yeoh Eik Den Student Id TP038999 Documents Version 1.0 1.0 Introduction In this introduction, we give an overview about this project report. As our objective, we will be bisected into different quantitative management techniques to examine and analyses the particular issue. We have defined the objective and explained the data for the past 10 years records that been identified by different areas such as metropolitan, city and town. We will be focus to used two-sample t-test for difference, correlation/multiple linear regression and forecasting techniques to discussed about the issue that been identified in 2.0 aims, objectives and hypotheses. Firstly, understand the demand of the fixed deposit been deposited by personal wealth from different areas. As Ministry of Finance, this are great to distingue the different of areas for future development and assist the people to improve of standard living. Secondly, investigation for the relationship of independent variable and multiple dependent variables in this case study. Where will be important to understand the influences of the dependent variables to the dependent variable. Finally, we would prepared for seasonal behavior for fixed deposit that been deposited to predict the trend analysis of this report. So, that Ministry of Finance can be forecast and predict the trend for the country economical. We conclude our results and provide the best fitted estimated model for forecast deposit rates of best fitted to the personal wealth at the end of the report. 2.0 Objective Our main objective in this report is to provide the significant test of data and forecast the deposit rates for different areas which involve in metropolitan, city and town. The outcomes of this study could be useful for Ministry of Finance in providing better insights of forecasting and understand the demand. We have collected the data and provided in the appendix 2.0. The study for this is to analyze by applying different quantitative management techniques. Basically we collected the data from 10 years since 2005 to 2014. 2.1 Define Hypotheses We identified the hypotheses for this report as below: First Hypothesis: Two Sample T-Test for Difference We use two sample t-test to confirm the assumption for the population variances to compare the average fixed income deposited per account in different areas which involved Metropolitan, City and Town. We test whether the demand is the same across this 3 areas. H0: p ≤ α, there are same demand across three areas. H1: p > α, there are different demand across three areas. Second Hypothesis: Correlation and Multiple Linear Regression Second hypothesis is to identify the independent variable with multiple dependent variables and the relationship between fixed deposit and government bond whether fixed deposit interest increase then bond decrease or the other way round. H0: p ≤ α, fixed deposit interest has relationship with government bond interest. H1: p > α, fixed deposit interest no relationship with government bond interest. Third Hypothesis: Forecasting Techniques Third hypothesis is find the quarter index that which quarter have most demand average. H0: Quarter 4 is the higher demand compare to other quarter for three areas average. H1: Quarter 4 is not the higher demand compare to other quarter for three areas average. 3.0 Finding and Discussion This section provided the hypothesis outcome. 3.1 Two Sample T-Test for Sample Descriptive statistics of all areas are calculated to find that whether the data set are following. The descriptive statistics of all the areas as follows: First we plot a new table to compare the difference areas, where you can find in Appendix 3. Then, we populated the result via excel and output as figure 3.1.2 below. Figure 3.1.2 Compare the two-sample test. Assume that α = 0.05; and, the hypothesis define as H0: p ≤ α, there are same demand across three areas. H1: p > α, there are different demand across three areas. The p-value for 3 results are almost close to 0. Therefore, for Metropolitan compare with City. The p-value for two-tail is p < α; we reject the null hypothesis. For City compare with Town and Metropolitan compare with Town, the result won’t be very different as p < α. Thus, we reject the null hypothesis. As conclusion, we reject the hypothesis for this two sample t-test as confirm our assumption that the population variances are almost equal. Which mean that, the demand for different areas is difference. 3.2 Correlation and Multiple Linear Regression From the case study, we define dependent variable as total personal wealth. However, the independent variables are average fixed deposit per account, fixed deposit interest and government bond interest. The population of regression model is: Multiple Regression: Y = a + b1X1 + b2X2 + b3X3 + u Whereby Y = total personal wealth; X1 = average fixed deposit per account; X2 = fixed deposit interest; X3 = government bond interest; a = the intercept; b = the slope; u = the regression residual; Assumed that the error u is independent with constant variance. The regression output has three components (Regression statistics, ANOVA, Regression coefficients) as show at figure 3.2.1 Hypothesis define as: H0: p ≤ α, fixed deposit interest has relationship with government bond interest. H1: p > α, fixed deposit interest no relationship with government bond interest. Figure 3.2.1 Summary output by excel statistics analysis for multiple linear regression. From the regression statistics table given: R2 = 0.7737 Correlation between Y is 0.8796 (when squared gives 0.7737) Adjusted R2 = 0.7679 The standard error here refers to the estimated standard deviation of the error term u. Mean that, 77.37% of the variation of Y around is explained by the regression of X1, X2, and X3. Remaining 22.63% will explained by other unknown factors. Next we test the confidence intervals for slope coefficients as 95% interval by the hypothesis of zero slope coefficient below: The coefficient of FD has estimated standard error of 0.6479, t-statistic of 19.7720 and p-value of almost close to 0. It is therefore statistically significant at significance level α = 0.05 as p < 0.05. For RFDP, we assume α = 0.05 and the p-value < 0.05. Thus, RFDP as well significant. For RGB, let’s assume α = 0.05 and the p-value > 0.05. Thus, RGB is insignificant. That proven, the relationship for this government bond is not significant in this multiple linear regression. The multiple regression for this is: Y = 1022.7661 + 12.8096X1 -172.1339X2 -50.1923X3 Meaning that, there is no relationship between fixed deposit interest and government bond interest. Therefore, we reject the null hypothesis. 3.3 Forecasting Techniques The hypothesis for this section is H0: Quarter 4 is the higher demand compare to other quarter for three areas average. H1: Quarter 4 is not the higher demand compare to other quarter for three areas average. The multiple regression that been populated at section 3.2 is Y = 1022.7661 + 12.8096X1 - 172.1339X2 - 50.1923X3 Therefore, linear trend been populated based on the multiple regression and fill in all the variables to generate the result. Figure 3.3.2 Linear Trend graph for 3 different areas and forecasting by seasonal chart. Figure 3.3.2 data are extract from table Figure 3.3.3, 3.3.4 & 3.3.5 that based on the linear trend populated by multiple regression. Figure 3.3.3 Seasonal estimates using a multiplicative model for Metropolitan For this figure 3.3.3, we know that Q4 average is the higher demand compare to other quarter. Thus, we do not reject null hypothesis for Metropolitan. Figure 3.3.4 Seasonal estimates using a multiplicative model for City For figure 3.3.4, the average forecast for Q4 is higher among other quarter in city. Thus, we do not reject the null hypothesis for city. Figure 3.3.5 Seasonal estimates using a multiplicative model for Town For figure 3.3.5, the average forecast for Q4 is higher among other quarter in town. Thus, we do not reject the null hypothesis for town. As conclusion, the 3 areas null hypothesis are true. Therefore, we do not reject null hypothesis as summary. 4.0 Conclusions & Recommendations Outcome Hypothesis 1 Reject Hypothesis 2 Reject Hypothesis 3 Do not reject Based on the outcome, confirm that the demand from different area have different demand. Whereby, there are no relationship between fixed interest rate and government bond. However, we prove that average of this 3 different area have the most demand during quarter 4. The recommendation for Ministry of Finance, prediction of the personal grow even year to year is increase. In the chart figure 3.3.2. They should focus to provide campaign or any awareness in town, to help town further improve their personal wealth. There are limitation on data that show the relationship for government bond. Thus, we do not know how much the personal wealth is involve for government bond. As mentioned in section 3.2, there are 22.63% will explained by other factors that influence the relationship for the personal wealth. This is quite large number that government does not able to predict and forecast accurately what will influence the personal wealth. 5.0 Reference Jon Curwin, Roger Slater and David Eadson. Quantitative Methods for Business Decisions, 7th Edition 2013. Publisher by Andrew Ashwin. By ET Bureau (12 Jan 2015, 02.31PM IST). Four things to check for in a fixed deposit. Retrieved from http://economictimes.indiatimes.com/wealth/fixed-deposits/four-things-to-check-for-in-a-fixed-deposit/articleshow/45832436.cms NDTV (02 May 2015). Why you should rethink fixed deposit investments. Retrieved from http://profit.ndtv.com/news/your-money/article-why-you-should-rethink-fixed-deposit-investments-757201 By Robert Brokamp. What is a bond? Retrieved from http://www.fool.com/bonds/bonds01.htm 6.0 Appendix 1.0 - VARIABLES Area : the area that the banks located RFDP : primary interest rate on fixed deposit (%) FD : average of fixed deposit per account (RM ‘000) PW : average personal wealth (RM ‘000) RGB : interest rates on government bonds (%) 6.0 Appendix 2.0 - Data Time Area RFDP FD PW RGB 2005Q1 Metropolitan 4.5 28 260 3.2 2005Q1 City 4.5 15 200 3.2 2005Q1 Town 4.5 5 120 3.2 2005Q2 Metropolitan 4.5 27 270 2.9 2005Q2 City 4.5 14 203 2.9 2005Q2 Town 4.5 5 123 2.9 2005Q3 Metropolitan 4.7 26 280 3.2 2005Q3 City 4.7 14 208 3.2 2005Q3 Town 4.7 6 124 3.2 2005Q4 Metropolitan 4.6 25 292 3 2005Q4 City 4.6 13 210 3 2005Q4 Town 4.6 6 127 3 2006Q1 Metropolitan 4.6 27 301 3.1 2006Q1 City 4.6 14 215 3.1 2006Q1 Town 4.6 6 129 3.1 2006Q2 Metropolitan 4.55 25 310 2.75 2006Q2 City 4.55 13 218 2.75 2006Q2 Town 4.55 6 131 2.75 2006Q3 Metropolitan 4.55 26 325 2.95 2006Q3 City 4.55 14 220 2.95 2006Q3 Town 4.55 5 133 2.95 2006Q4 Metropolitan 4.55 25 332 3.2 2006Q4 City 4.55 13 225 3.2 2006Q4 Town 4.55 4 134 3.2 2007Q1 Metropolitan 5.1 30 339 3 2007Q1 City 5.1 18 228 3 2007Q1 Town 5.1 10 135 3 2007Q2 Metropolitan 5.1 32 345 3.1 2007Q2 City 5.1 19 230 3.1 2007Q2 Town 5.1 10 129 3.1 2007Q3 Metropolitan 4.9 31 350 2.75 2007Q3 City 4.9 17 232 2.75 2007Q3 Town 4.9 9 134 2.75 2007Q4 Metropolitan 4.75 23 360 2.9 2007Q4 City 4.75 14 235 2.9 2007Q4 Town 4.75 7 138 2.9 2008Q1 Metropolitan 4.75 24 367 2.95 2008Q1 City 4.75 15 238 2.95 2008Q1 Town 4.75 8 140 2.95 2008Q2 Metropolitan 4.9 32 369 2.75 2008Q2 City 4.9 17 240 2.75 2008Q2 Town 4.9 9 142 2.75 2008Q3 Metropolitan 4.9 29 371 2.95 2008Q3 City 4.9 18 242 2.95 2008Q3 Town 4.9 10 144 2.95 2008Q4 Metropolitan 4.82 24 373 3 2008Q4 City 4.82 17 250 3 2008Q4 Town 4.82 8 145 3 2009Q1 Metropolitan 4.82 23 380 2.9 2009Q1 City 4.82 16 251 2.9 2009Q1 Town 4.82 8 146 2.9 2009Q2 Metropolitan 4.73 22 390 3.1 2009Q2 City 4.73 15 253 3.1 2009Q2 Town 4.73 7 148 3.1 2009Q3 Metropolitan 4.66 22 402 3.2 2009Q3 City 4.66 15 255 3.2 2009Q3 Town 4.66 6 149 3.2 2009Q4 Metropolitan 4.75 24 410 2.95 2009Q4 City 4.75 14 256 2.95 2009Q4 Town 4.75 7 150 2.95 2010Q1 Metropolitan 4.6 23 417 3.1 2010Q1 City 4.6 13 257 3.1 2010Q1 Town 4.6 7 151 3.1 2010Q2 Metropolitan 4.58 23 421 2.75 2010Q2 City 4.58 12 260 2.75 2010Q2 Town 4.58 6 152 2.75 2010Q3 Metropolitan 4.7 26 425 2.95 2010Q3 City 4.7 14 262 2.95 2010Q3 Town 4.7 7 153 2.95 2010Q4 Metropolitan 4.7 25 430 3 2010Q4 City 4.7 15 264 3 2010Q4 Town 4.7 7 153 3 2011Q1 Metropolitan 4.75 24 440 2.85 2011Q1 City 4.75 15 265 2.85 2011Q1 Town 4.75 8 154 2.85 2011Q2 Metropolitan 4.65 23 450 3.2 2011Q2 City 4.65 15 266 3.2 2011Q2 Town 4.65 6 155 3.2 2011Q3 Metropolitan 4.5 22 453 2.85 2011Q3 City 4.5 15 267 2.85 2011Q3 Town 4.5 5 157 2.85 2011Q4 Metropolitan 4.45 21 451 2.9 2011Q4 City 4.45 14 270 2.9 2011Q4 Town 4.45 4 158 2.9 2012Q1 Metropolitan 4.45 21 462 2.85 2012Q1 City 4.45 15 271 2.85 2012Q1 Town 4.45 4 160 2.85 2012Q2 Metropolitan 5 33 467 2.75 2012Q2 City 5 18 273 2.75 2012Q2 Town 5 10 162 2.75 2012Q3 Metropolitan 4.75 25 469 3 2012Q3 City 4.75 17 275 3 2012Q3 Town 4.75 7 163 3 2012Q4 Metropolitan 4.58 21 474 2.95 2012Q4 City 4.58 16 276 2.95 2012Q4 Town 4.58 5 163 2.95 2013Q1 Metropolitan 4.5 24 480 2.85 2013Q1 City 4.5 15 278 2.85 2013Q1 Town 4.5 5 164 2.85 2013Q2 Metropolitan 4.3 22 482 2.9 2013Q2 City 4.3 15 280 2.9 2013Q2 Town 4.3 3 165 2.9 2013Q3 Metropolitan 4.6 23 485 3 2013Q3 City 4.6 14 281 3 2013Q3 Town 4.6 6 166 3 2013Q4 Metropolitan 4.6 24 490 2.85 2013Q4 City 4.6 13 282 2.85 2013Q4 Town 4.6 5 167 2.85 2014Q1 Metropolitan 4.48 23 493 3.2 2014Q1 City 4.48 12 284 3.2 2014Q1 Town 4.48 4 168 3.2 2014Q2 Metropolitan 4.48 24 496 2.95 2014Q2 City 4.48 12 286 2.95 2014Q2 Town 4.48 4 170 2.95 2014Q3 Metropolitan 4.75 24 501 2.85 2014Q3 City 4.75 14 288 2.85 2014Q3 Town 4.75 7 171 2.85 2014Q4 Metropolitan 4.6 24 503 3 2014Q4 City 4.6 14 292 3 2014Q4 Town 4.6 6 172 3 6.0 Appendix 3.0 Staffordshire University 12 Prepared by Yeoh Eik Den