数学report.docx

1、数学reportThe Research of New House Sales in AustraliaAnd Its Future Trend AnalysisClass 03 房子微 SallyClass 03 姚晗 DestinyClass 03 刘丁 Dawn Date : 03 / 06 / 2014Content1.0 Introduction.22.0 Calculation and Analysis 22.1 Likely Influence Factors 32.1.1 Season 3v Steps and calculations 3v Result 5v Analysi

2、s 52.1.2 Wages 6v Steps and calculations 6v Result 8v Analysis 82.2 Future Trend Analysis 9v Steps and calculations 9v Result: 11v Analysis 113.0 Conclusion and Recommendation 12Reference 131.0 IntroductionIn recent years, with the increasing population, the demand of some necessities of life such a

3、s houses is going up at the same time. Therefore, the problem of housing has already become a focus of attention around the world. This report will study the house sales issue in Australia by analyzing two likely factors (season and wages) which may influence the amount of new house sales from year

4、2009 to 2013, and predicting the future trend of house selling. The aim of it is to help the land agents deal well with the relation between house supply and house demand and gain more profits. The analysis in this report will be divided into three parts. The first part will analyze the influence of

5、 season using the method of index number. The next part will show the relation between people wages and the new house sales with the method of correlation and regression analysis. The last part forecast the future trend by the method of time series analysis. The data used in this report are the numb

6、er of Australian every months new house sales and average wages of local people from 2009 to 2013. All these data are secondary data which were collected in the website called Trading economics. ( ).2.0 Calculation and AnalysisIn order to balance the new house supply and demand, we can do two things

7、 by calculating and analysis. The one is that we need to know what will influence the new house sales in Australia, and change the amount of supply rely on these factors to exactly satisfy customers demand and avoid surplus or shortage. The other one is to predict the future trend of new house sales

8、, and it can also help achieve the same goal that mentioned above. 2.1 Likely Influence Factors Season and wages are two common factors which will influence purchasing power. Therefore, we assume they will influence new house sales as well, and then, we do some calculation and analysis to prove our

9、assumption. 2.1.1 Season In this section, we use the index number analysis to interpret seasonal variation. The process of removing the seasonal influences from data is called deseasonalization of data or seasonal adjustment. In order to do this we can use a seasonal index. The seasonal index is a n

10、umber which is a weighted proportion of the annual numbers that occur in a particular quarter or time period (VICTORIAUNIVERSITY 2013, p299). Therefore, this report uses the seasonal index number to analyze the influence of season to the new house sales. The simple average method is used to calculat

11、e the seasonal index.v Steps and calculations1. Collect the new house sales for each months from 2009 to 2013 on the website.2009201020112012201316667756765225230500827200720866235344480637414734770094824499447496778870365133532756983733168705028537367001684762655065576677024634857014787539987855613

12、45785451057129751760345595435059711070026438568442645698117060636661144502590312687163855645481559592. Take three month as a quarter, and calculate the average amount of each quarter.20092010201120122013Q12128122122201541539814808Q22148021966201711522616466Q32239618516170811364717082Q420933191891744

13、31358117560Mean=sum/amountmeanQ123440.75Q223827.25Q322180.5Q422176.53. Calculate the mean of all periods.mean of all periods22906.254. Calculate index number of each quarter.Seasonal index number=mean of each quarter/mean of all periods*100indexQ11.023334243Q21.040207367Q30.968316508Q40.9681418835.

14、Calculate the deseasonalized value of every quarter from 2009 to 2013.Deseasonalized value=actual value/seasonal index number*10020092010201120122013Q120795.7469921617.5703619694.4450415046.8921614470.34545Q220649.7287821116.9433119391.3258514637.4660315829.53604Q323128.801219121.8468917639.89343140

15、93.5323317640.92615Q421621.8308219820.4419718016.987314027.9025718137.837356. Compare the actual value to deseasonalized value from 2009 to 2013 (the rank of each quarter).Rank200920123311242211334244201020131144223344223311201121124433v ResultThe trend of 3 out of 5 years are not change (2010, 2012

16、, 2013), and the other 2 years are also only change for a little (2009, 2011).v AnalysisWe can compared the deseasonalized value to the actual value of each year, if it shows the same trend, it means season makes no different to the sales; however, if they are different, it means season is an import

17、ant factor to the new house sales.In this report, we compared the 2 values, and found that the trends of the 2 values are quite similar. Therefore, this report argues that the factor of season have influence on the new house sales in Australia from 2009 to 2013, but it only have very little influenc

18、e. Thus, season may not be an essential factor which can influence new house sales in Australia.2.1.2 WagesIn this section, we use the correlation and regression analysis to interpret the relation between new house sales and peoples wages. Correlation and regression analysis is used to describe the

19、strength and direction of the relationship between two variables (VICTORIAUNIVERSITY 2013, p233). When study the relationship between new house sales and peoples, first, in regression analysis part, we decide to draw the regression line by eye just to help us have a rough estimate of their relation;

20、 and then, in correlation analysis part, we decide to use Pearson Product-Moment Correlation Coefficient (r) to know their correlation in detail. v Steps and calculations1. We let the average wages and amount of new house sales to be the two variables x and y respectively and draw a scatter diagram.

21、 2. We do a rough estimate for their relation by drawing a regression line by eye.It can be seen clearly that there is a negative relation between the new house sales and peoples wages.3. We calculate the correlation coefficient to help us know the degree of correlation by using the formula: . 4. We

22、 test the significance of correlation coefficient by using the p value.We can get N=5, so N-2 =3, and0.830.805 v ResultAfter the calculation, we get the correlation coefficient is -0.83 which can represent a high negative correlation between wages and new house sales. Then we test significance of co

23、rrelation coefficient by using the p value which shows how likely the relationship is due to chance. Our sample size is 5 so the degrees of freedom is 3, then we find the p value to compare with 0.83. We can find 0.830.805 that means the relationship is significant at the 0.1 level and p 0.1.v Analy

24、sisThe result of calculation has shown us the high correlation between Australian new house sales and peoples wages which means wages is an important influence factor of new house sales. Many people may wonder why the more money people earn the less houses they demand. The reason is that house is a

25、durable and necessary product for people. When they earn more money and it is enough for them to buy their houses in this year, they can buy new house in this year immediately because they need houses to live; and next year, although their income is still increasing, they will not have to buy anothe

26、r new house because one house is enough for them, and it can be used in several decades. As a result , more wages make more people have ability to buy their houses in “this year” and less in “next year”, thus, it shows a negative relation between new house sales and peoples wages.2.2 Future Trend An

27、alysis In this section, we use the time series analysis to forecast the number of Australian new house sales in the future. Time series analysis is used to predict what may happen in the future on the basis of what has been happening in the pass (VICTORIAUNIVERSITY 2013, p264). When we are studying

28、the future trend of new house sales by calculation, the Least Squares Method is adopted.v Steps and calculations1. Plot the sales of new houses from 2009 to 2013 on a graph in polygon format. Join them in a dotted line.2. Make a frequency table to tabulate this information.3. Code the time on x-axis

29、. Because five years is an odd number, label the midpoint as 0 and other points as positive or negative whole number deviation from 0. Accordingly, the coded time are -2, -1, 0, 1and 2.YearSales (y)Coded Time (x)(xy)(x) 200986,090-2-172,1804201081,793-1-81,7931201174,854000201257,852157,8521201365,9162131,8324Total366,5050-64,289104. Calculate the value of a and b using the formula. Then obtain the trend line .5. Find three points values with time codes of -2, 0 and 2 on the graph.-2 (2009year)0 (2011year)2 (2013year)73,301-6,428.9(-2)73,301-6,428.9(0)73,301-6,428