Business Statistics BayCoast Real Estate Agents

Question: Discuss about theBusiness Statisticsfor BayCoast Real Estate Agents. Answer: Case Study Agents (BCREA ) business has grown. However, the principals are aware that various factors affect the selling prices of houses within the city of Melbourne. They are therefore faced with the challenge of applying modern techniques of estimating the selling price of houses. Among the factors that affect the selling price of houses within the city are bay views, size of the house, and size of the block and design of fittings in the property. In particular, BCREA would like to determine whether street scape appeal has any significant relationship with the price of the house because it is considered that a street that is more attractive is preferred by potential buyers. The hypothesis therefore, to be tested would be; H0 :There is a significant relationship between the streetscape appeal and the selling price of a house HA : There is no significant relationship between the streetscape appeal and the selling price of a house The requirement is to find out whether there is any significant association between streetwise appeal (x) and the selling price of houses (y). The degree of variability between streetwise appeal and selling price is also important to determine the percentage of association between the two variables. That is, how much change in selling price of a house can be accounted for by a change in streetwise appeal? a) Lucey (1996) notes that finding the line of best fit mathematically, it is prudent to calculate a line that reduces the total of the squared deviations of the actual observations from the calculated line.This is the least squares method of linear regression. The least squares method of linear regression can be extended to equations with multiple independent variables as; The line of best fit is the multiple regression line Lucey (1996) contends that in situations whereby the value of r2 in a simple linear regression is not enough indicates this equation will be inadequate to predict the value of y. The simple linear equation is expressed as; y = a + bx Where y = the dependent variable or predictor a = the constant or intercept b = the slope or gradient of the regression line equivalent to the variable element x = the independent variable In the question, involves two variables, that is the dependent (the selling price of houses in the city of Baycoast) and one independent variable (the streetwise appeal measured by a scale of o to 10 from lowest appeal to highest appeal). Therefore, we use the equation of the form, y = a + bx. The equation of least squares regression line is derived from cell B19 that represents (a) the intercept and B20 that represents (b) the slope of the independent variable streetwise appeal. Therefore, to substitute the equation, the regression equation will be; y = 183.26 + 122.32(x) Kingoriah (2004) notes that once the regression equation is computed the expectation is that the equation will be used to predict values of x and y. Another assumption is that the relationship between the two variables is within the realm of the model The standard error of estimate is used to create a confidence interval along the regression line instead of one point estimate such as the population or sample mean. It involves estimating the true standard deviation. Whereas the term standard deviation is used for a population, the standard error is used for a sample. In essence, therefore standard deviation and standard error is the same thing. The regression model shows a standard error of the estimate associated with the beta coefficient (b) or street (cell B20) as 10.77 contained in cell C20. Since the coefficient is large compared to its standard error of the estimate suggests is different from zero. This test is meant to determine whether there is a significant linear relationship between the independent variable x (streetwise appeal) and the dependent variable y (selling price of houses). In this case the hypotheses can be stated as follows; H0 : : There is no significant linear relationship between the independent variable x and the dependent variable y HA : : There is a significant linear relationship between the independent variable x and the dependent variable y H0 : = 0 HA : 0 Where there is a significant linear relationship between the independent variable x and the dependent variable y, then 0 The significance level is 5% (0.05) since the confidence level used is 95% (0.95) that is, 1 0.95 = 0.05. According to the regression results, at one degree of freedom (df) cell B13, the independent variable x has a test statistic t stat (cell C13) that is associated with a p-value of less than zero (cell F20). Therefore, we reject the null hypothesis. We conclude that there is sufficient evidence to suggest that there is a significant linear relationship between the independent variable x and the dependent variable y (tstat= 11.35, p 0) The coefficient of determination denoted by r2 is used to determine how the change in one variable can be associated or explained with difference of another variable and it is normally between zero and one.. That is, to identify the intensity or degree of the linear relationship between the variables. In this case, the coefficient of determination is 0.52 contained in cell B5 in the diagram. This essentially means that 52% of the data points should be within the regression line or put another way 52% of the variability in selling price of the houses can be explained by streetwise appeal. As such street rating appears not to be a very good predictor. Regression analysis was used to develop a model for predicting selling price of houses in Baycourt area using the streetscape appeal ranging from zero ( lowest appeal ) to ten (the highest appeal). The basic descriptive statistics and regression coefficient are shown in the figure above. The predictor variable had a significant (p 0.05) correlation with selling price effect in the model. The predictor variable was able to account for 52% of the variance in the selling price of houses (f 128.9, r2 = 0.52, 95% CI [ 100.98, 143.65] ). In this situation, we are 95% confident that the true increase in selling price of houses for an increase in streetscape appeal is between 100.98 and 143.64 for a sample of 120 houses. Whereas zero is not inclusive in the interval, there is reason to believe that there is a linear relationship between streetscape appeal and selling price of houses at significance level of .05. Based on the analysis, it is recommended that the management consider using other factors they are aware affect the price of a house. This is because, although streetscape appeal has a linear relationship with the selling price, the degree of relationship is not as strong (at 52%) that is, it is just above average. This essentially means that the other 48% of the residents may not necessarily be influenced by the location in order to purchase a house. The management therefore, should consider using the other factors in conjunction with streetscape appeal to predict the selling price of the houses. References Kingoriah, GK. 2004,Fundamentals of applied statistics. Nairobi, Kenya: The Jomo Kenyatta Foundation. Lucey, T. 1996,Quantitative techniques. United Kingdom: Cengage Learning EMEA.