Which Factors Most Influence the Variable Rate of Home Loans - Essay Example

EXECUTIVE SUMMARY This exercise provides an opportunity to deepen understanding of the relevant statistical concepts and techniques by applying them to real world data on home loan interest rates. Home loans are offered by banks and number of other institutions. Currently, numerous home loan products are available in the market, each with a particular interest rate and varying features. This report is aimed to summarise, analyse and interpret the datasets noting any key features and to determine which factors most influence the variable rate of these home loans. During the analysis, descriptive statistical indicators like mean, median, skewness and standard deviation were calculated. Also different tools like Multi-vari Charts, Correlation, Regression Analysis and One-Way ANOVA were used to interpret any key features of the data available. The details of these analysis in contained in appendices attached to this report while comprehensive discussion is made part of this report. To carry out statistical analysis, Minitab Statistics Software 15.1 was used which is a comprehensive statistical computer package available to the researchers. Minitab includes descriptive statistics, descriptive ratio statistics, bivariate statistics, and the prediction for both numerical outcomes and identifying groups in the base software. Introduction to Engineering Statistics and Six Sigma by Theodore (2006) alongwith other books was the main reference guide to conduct the above mentioned analysis. TECHNICAL REPORT Descriptive Statistics of 90 Day Bank Accepted Bill Statistical analysis of 90 Day Bank Accepted Bill revealed mean of 9.056 and standard deviation of 4.110 with variance 16.890. The median is 7.6 to with mode 5.63 and 5.8. Minimum value was 3.740 and maximum 21.750 with range 18.010. The distribution is positively skewed with skewness value of 0.85. Read Appendix ‘A’. Time Series Plot for 90 Day Bank Accepted Bill The plot indicated that the values continued to increase till September 1989 and then gradually started decreasing till October 1993 and finally settled between 8.55 and 4.55 after October 1993. Largest values were seen 21.75 and 21.39 in May 1974 and April 1982 while lowest value was 3.74 in January 2009. Read Appendix ‘B’. One-way ANOVA: 90 Day Bank Accepted Bill Rate versus Year A one-way ANOVA tests the hypothesis that the means of several populations are equal. The method is an extension of the two-sample t-test, specifically for the case where the population variances are assumed to be equal. If P is larger than the α-level you have selected, the means are not significantly different (Theodore, 2006). The p-value for the year is 0.000 for α-level of 0.05. Thus, it can be concluded that there are significant differences in 90 Day Bank Accepted Bill Rate for all years. For the data, S is 1.223, R is 91.89%, and adjusted R equals 91.15%. Read Appendix ‘C’. One-way ANOVA: 90 day Bank Accepted Bill Rate versus Month In this case, the p-value for the year is 0.978 for α-level of 0.05. Thus, it can be concluded that there is no significant difference in 90 Day Bank Accepted Bill Rate for months (Theodore, 2006). For the data, S is 4.142, R is 0.79%, and adjusted R equals 0.00%. Read Appendix ‘D’. Descriptive Statistics of Bank Std Variable Rate Statistical analysis of Bank Std Variable Rate revealed mean of 9.796 and standard deviation of 2.936 with variance 8.620. The median is 9.375 to with mode 9.875. Minimum value was 5.875 and maximum 17.000 with range 11.125. The distribution is positively skewed with skewness value of 0.77. Read Appendix ‘E’. Time Series Plot for “Bank Standard Variable Rate” The graph depicted that the rate was lowest in June 1969 with value 5.88 and gradually reached 17.00 in June 1989; however, it started declining after March 1990 and reached a value of 6.85 in December 2008. Read Appendix ‘F’. One-way ANOVA: Bank Std Variable Rate versus Year The p-value for the year is 0.000 for α-level of 0.05. Thus, it can be concluded that there are significant differences in Bank Std Variable Rate for all years (Theodore, 2006). For the data, S is 0.5003, R is 97.34%, and adjusted R equals 97.10%. Read Appendix ‘G’. One-way ANOVA: Bank Std Variable Rate versus Month In this case, the p-value for the year is 1.000 for α-level of 0.05. Thus, it can be concluded that there is no significant difference in Bank Std Variable Rate for months (Theodore, 2006). For the data, S is 2.97, R is 0.02%, and adjusted R equals 0.00%. Read Appendix ‘H’. Pearson’s Correlation and Regression Analysis : 90 day Bank Accepted Bill Rate and Bank Std Variable Pearson correlation of 90 day Bank Accepted Bill Rate and Bank Std Variable was found to be 0.842 with p-value = 0.000 which is significant. Thus a linear regression analysis was conducted. From the regression analysis, it was concluded that their exists a strong linear relationship between the two variables since Bank Std Variable Rate has a p-value of 0.000 which is less than α-level 0.05. For the model S is 2.22, R-Sq 70.9% and R-Sq(adj) is 70.8%. Read Appendix ‘I’. Descriptive Statistics: Variable Rate Statistical analysis of Variable Rate (Sheet2) revealed mean of 5.801 and standard deviation of 0.797 with variance 8.620. The median is 5.65 with mode 5.91. Minimum value was 4.88 and maximum 10.5 with range 5.17. The distribution is positively skewed with skewness value of 2.49. Read Appendix ‘J’. Descriptive Statistics: 5 Year Cost $ Statistical analysis of 5 Year Cost (Sheet2) revealed mean of 95795 and standard deviation of 7690. The median is 94057 with mode 95833.5. Minimum value was 87951 and maximum 138284 with range 50333. The distribution is positively skewed with skewness value of 2.67. Read Appendix ‘K’. Descriptive Statistics: Repay. Amount (Monthly)$ Statistical analysis of Repay Amount (Monthly) revealed mean of 1582.6 and standard deviation of 125.8. The median is 1557.7 with mode 1597.03. Minimum value was 1444.1 and maximum 2280.6 with range 836.5. The distribution is positively skewed with skewness value of 2.65. Read Appendix ‘L’. Pearson’s Correlations and Regression analysis: 5 Year Cost $, Variable Rate Pearson correlation of 5 Year Cost $ and Variable Rate was found to be 0.997 with P-Value of 0.000. Read Appendix ‘R’. From the regression analysis, it was concluded that their exists a strong linear relationship between the two variables since Variable Rate has a p-value of 0.000 which is less than α-level 0.05 (Lloyd, 2006). For the model S is 595.122, R-Sq 99.4% and R-Sq(adj) is 99.4%. Read Appendix ‘M’. Pearson’s Correlations and Regression Analysis: Variable Rate, Repay. Amount (Monthly) $ Pearson correlation of Variable Rate and Repay. Amount (Monthly)$ was 1.000 with P-Value = 0.000. From the regression analysis, it was concluded that their exists a strong linear relationship between the two variables since Variable Rate has a p-value of 0.000 which is less than α-level 0.05 (Lloyd, 2006). For the model S is 3.63, R-Sq 99.9% and R-Sq(adj) is 99.9%. Read Appendix ‘N’. Pearson’s Correlations and Regression Analysis: 5 Year Cost $, Repay. Amount (Monthly) $ Pearson correlation of 5 Year Cost $ and Repay. Amount (Monthly)$ was 0.998 with P-Value = 0.000. From the regression analysis, it was concluded that their exists a strong linear relationship between the two variables since “5 Year Cost” has a p-value of 0.000 which is less than α-level 0.05 (Lloyd, 2006). For the model S is 8.55, R-Sq 99.5% and R-Sq(adj) is 99.5%. Read Appendix ‘O’. Variable Rate and Institution Type From multi-vari charts, it was found that BS institutions had least variable rate while ‘O’ type had the highest (Hawkins, 1980). Also one-way ANOVA revealed that p-value for Institution Type was 0.000 less than α-level of 0.05. Thus it could be concluded that there was a difference in variable rates for institutions types since ‘O’ type had significantly higher rates than others (Theodore, 2006). Read Appendix ‘P’. Variable Rate and Redraw Multi-vari charts revealed that organization with No Redraw policy had lower variable rate than those who allowed Redraw (Hawkins, 1980). However, ANOVA concluded no significant difference in the mean variable rates for two types since p-value for Redraw was 0.313 greater than α-level of 0.05 (Theodore, 2006). Read Appendix ‘Q’. Variable Rate and Portability Multi-vari charts revealed that organization with No Portability policy had lower variable rate than those who allowed Portability (Hawkins, 1980). However, ANOVA concluded no significant difference in the mean variable rates for two types since p-value for Portability was 0.487 greater than α-level of 0.05 (Theodore, 2006). Read Appendix ‘R’. Variable Rate and Mortgage Offset Multi-vari charts revealed that organization with No Mortgage Offset had greater variable rate than those with Mortgage Offset (Hawkins, 1980). However, ANOVA concluded no significant difference in the mean variable rates for two types since p-value for Mortgage Offset was 0.242 greater than α-level of 0.05 (Theodore, 2006). Read Appendix ‘S’. Variable Rate and 100% Offset Multi-vari charts revealed that organization with No 100% Offset had greater variable rate than those with 100% Offset (Hawkins, 1980). However, ANOVA concluded no significant difference in the mean variable rates for two types since p-value for Mortgage Offset was 0.389 greater than α-level of 0.05 (Theodore, 2006). Read Appendix ‘T’. Variable Rate and Redraw Fee Multi-vari charts showed that highest variable rate was 5.95 for Redraw fee of 30$ and lowest was 4.95 for Redraw fee of 9.95 (Hawkins, 1980). Also one-way ANOVA confirmed p-value of 0.575 greater than α-level of 0.05 indicating that there was no significant difference in means values of variable rates for different Redraw fee (Theodore, 2006). Read Appendix ‘U’. Variable Rate and Portability Fee Multi-vari charts showed that highest variable rate was 7.92 for Portability fee of 765$ and lowest was 4.95 for Portability fee of 595$ (Hawkins, 1980). One-way ANOVA confirmed p-value of 0.025 less than α-level of 0.05 indicating that there was significant difference in means values of variable rates for different Portability fee (Theodore, 2006). Read Appendix ‘V’. Variable Rate and Application Fee Multi-vari charts showed that highest variable rate was 6.85 for Application fee of 545$ and lowest was 4.88 for Application fee of 1075$ (Hawkins, 1980). One-way ANOVA confirmed p-value of 0.639 greater than α-level of 0.05 indicating that there was no significant difference in means values of variable rates for different Application fee (Theodore, 2006). Read Appendix ‘W’. Variable Rate and Valuation Fee Multi-vari charts showed that highest variable rate was 7.77 for Valuation fee of 265$ and lowest was 5.24 for Valuation fee of 175$ (Hawkins, 1980). One-way ANOVA confirmed p-value of 0.000 less than α-level of 0.05 indicating that there was significant difference in means values of variable rates for different Valuation fee (Theodore, 2006). Read Appendix ‘X’. Variable Rate and Legal Fee Multi-vari charts showed that highest variable rate was 7.85 for Legal fee of 275$ and lowest was 5.03 for Legal fee of 430$ (Hawkins, 1980). One-way ANOVA confirmed p-value of 0.000 less than α-level of 0.05 indicating that there was significant difference in means values of variable rates for different Legal fee (Theodore, 2006). Read Appendix ‘Y’. Variable Rate and Settlement Fee Multi-vari charts showed that highest variable rate was 8.55 for Settlement fee of 1025$ and lowest was 4.95 for Settlement fee of 299.95$ (Hawkins, 1980). One-way ANOVA confirmed p-value of 0.000 less than α-level of 0.05 indicating that there was significant difference in means values of variable rates for different Settlement fee (Theodore, 2006). Read Appendix ‘Z’. Variable Fee and Annual Service Fee Multi-vari charts showed that highest variable rate was 6.44 for Annual Service fee of 24$ and 50$ and lowest was 5.01 for Annual Service fee of 345$. One-way ANOVA confirmed p-value of 0.796 greater than α-level of 0.05 indicating that there was no significant difference in means values of variable rates for different Annual Service fee (Theodore, 2006). Read Appendix ‘AA’. Variable Fee and Exit Fee Multi-vari charts showed that highest variable rate was 7.92 for Exit fee of 520$ and lowest was 5.05 for Exit fee of 600$. One-way ANOVA confirmed p-value of 0.366 greater than α-level of 0.05 indicating that there was no significant difference in means values of variable rates for different Exit fee (Theodore, 2006). Read Appendix ‘AB’. REFERENCES Theodore, T. A. (2006). Introduction to Engineering Statistics and Six Sigma. London, UK: Springer-Verlag. Hawkins, D. (1980). Identification of Outliers. London, UK: Chapman and Hall. Lloyd, R. (2006). Statistics for the Utterly Confused. New York, NY : McGraw Hill. Read More