Data representing the bill amount and days overdue for 96 customers, evenly split between residential and commercial will be used to determine whether a relationship exists. The data is run separately for each customer group - residential or commercial. The statistical significance of the data in the table generated is tested to determine whether the relationship is statistically significant. The Regression Model In order to determine whether a relationship exists, a regression model is required. The equation for this model is as follows: Y = a + bX Where: a represents the point of intercept with the Y axis b is a regression coefficient which represents the net change in Y for each unit of change in X The model is dealt with separately for residential and commercial customers. Commercial Customers The result for commercial customers which is shown in Appendix 1 indicates that there is a 96.58% correlation (represented by Multiple R) between the size of the bill and the number of days overdue. Multicollinearity does not exist as there is only one explanatory variable. Gujarati (1995) indicates that multicollinearity in its broadest sense relates to the existence of an perfect or exact linear relationship among some or all explanatory (X) variables of a regression model as well as where the X variables are inter-correlated but not perfectly. The coefficient of determination (R squared or the correlation coefficient squared) is 95.65% and indicates that 95.65% of the change in the dependent
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2 pages (500 words)Research Proposal
variable Y (the number of days overdue) depends on the change in the independent variable X (the bill size). It is a measure of the goodness of fit (ie how well the sample regression line fits the data) (Gujarati 1995). Adjusted R squared which is 95.56% is the coefficient of determination (R squared) adjusted by 1 degree of freedom (df). It provides a better measure of how well the sample regression line fits the data. According to Mason and Lind (1996) the standard error of estimate in regression analysis which is 3.2205 measures the variation about the regression line. The regression equation for the commercial customers is: Y = 101.7582 – 0.1910X This equation indicates that the intercept is 101.7582 and the slope of the coefficient of X is -0.1910. The equation indicates that as the size of the bill increases the number of days the payment becomes late decreases. This suggests an inverse relationship between bill size and days overdue. According to Madura (2006, p. 754) the slope coefficient of -0.19 suggests that every 1 percent change in the days overdue is associated with a 0.19 per cent change in the opposite direction in the bill size. The graph below provides a better picture of this scenario. The graph shows that as the bill amount increases the number of days decrease. The result for customers which is shown in Appendix 2 indicates that there is a 96.58% correlation between bill size and the number of days overdue. The information also indicates that the 93.14% of the change in the days overdue is explained by the size of the bill and that the variation from the regression line is 3.5152. Residential Customers The equation relating to the residential customers is: Y = 2.2096 + 0.1657X This equation indicates that the regression line crosses the Y axis at 2.2096 and that the slope of the X coefficient is a positive 0.1657. This information indicates that the days overdue is directly related to the bill size and so for every 1 percent c
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639450 C32 Memorandum To: QSCA Management From: QSCA Consultant Subject: Relationship between Size of Bills and Number of Days to Collect Introduction The purpose of this memo is to provide information that will enable QSCA to increase the probability of earning high profits…