STATISTICS FOR FINANCIAL DECISIONS

Table of Contents

Introduction. 2

Task 1. 3

Task 2. 3

a) Providing a summary of market price and age of the house. 3

b) Describing the shape of the distribution for the age of the house as well as the market price. 5

c. Analysis of the market price of average population. 6

d) Construction of confidence. 7

e) Rationalisation of the model 7

f. Analysis of scatter plot 8

g) Summary of the regression model 11

h) A Simple Linear regression model 12

i) Interpretation of the slope coefficient 13

j. Explanation of the coefficient determination. 13

k. Interpretation of the interval 14

l) Comparison among the multiple regression model and simple linear regression model 15

m) Prediction about the house prices. 16

n) Decision obtained from the hypothesis test 16

o) Hypothesis formulation, statistical decision. 16

Conclusion. 17

References. 18

Appendices. 20

Appendix 1: Data set 20

 

Introduction

Statistical analysis is referred to as scrutinizing and collecting data which helps in taking decisions. Financial decisions are taken by the management to make decisions regarding finance in an organization. The financial decision is taken by the financial manager of an enterprise which helps in taking decisions regarding a large amount of finance that is involved in an organization. This assignment is focusing on price property with the help of Sydney and with the help of these implications and analysis will be done. Moreover, this analysis would help in taking business and financial decisions. The analysis is based on dependent and independent variables that have been collected. 

Task 1

In this task, it has been asked to select the data from the provided, thus, 50 unique numbers of properties have been selected with the help of ID number. Moreover, the selected data has been provided in the excel file.

[Refer to Appendix 1]   

Task 2

a) Providing a summary of market price and age of the house

Summary Statistics
Age of house (years)		Market Price ($000)
Mean	18.7254342	Mean	804.023
Standard Error	1.75856097	Standard Error	5.91356
Median	18.4492682	Median	797.071
Mode	#N/A	Mode	#N/A
Standard Deviation	12.4349039	Standard Deviation	41.8152
Sample Variance	154.626835	Sample Variance	1748.51
Kurtosis	-0.8569126	Kurtosis	-0.4981
Skewness	0.35894668	Skewness	0.46981
Range	45.3771129	Range	166.866
Minimum	-0.4119335	Minimum	745.144
Maximum	44.9651794	Maximum	912.01
Sum	936.271708	Sum	40201.2
Count	50	Count	50

Table 1: Summary Statistics

(Source: Created by the Researcher)

In the above table, the statistical summary of market price and age of house has been shown, with respect of this table it can be determined that mean in the age of the house is showing the similar value which indicates that the balance point of data is resembled and according to this average can occur. While considering skewness in the above table, it can be concluded that it has a value of 0.35, this value suggests that skewness is approximately symmetric. These data have been collected with 50 data which have been selected in task 1.

The table is determining the means of the market price which is showing the different value which indicates the positive point of skewness and this occurs because the data at the end is outlining higher value. While considering skewness in the above table, it can be concluded that it has a value of 0.46981. This value suggests that skewness is approximately symmetric.

b) Describing the shape of the distribution for the age of the house as well as the market price

The shape of the distribution is several top points and different allocated points shown in one graph (Komsta & Novomestky, 2015).  

Figure 1: Graph for the age of house and market price

(Source: Created by the Researcher)

According to the above figure, it can be concluded that the market price and age of the house are showing different shapes. The shape of the market price is downward sloping where is the age of the house is having high fluctuation. Both the lines in the graph are shown differently, therefore, it can be said that the shape of the distribution is inverse.

c. Analysis of the market price of average population

In this context, it is possible to say that average population’s market price can be detected using the ordinal data (Little & Rubin, 2019). In this regard, it has been identified that the average market price is 777.0244 dollars. As for this reason, it can be said that there is no changes in the market price. It is because; the given average market price of population is 777 dollars. On the other hand, the calculated market price is 777.0244 dollars.

 

d) Construction of confidence

Standard error = sample / sqrt (population)

= 41.81/ sqrt (50)

= 5.91

In the above calculation, 41.81 is the standard deviation of the market prices of housing property.

The alpha (?) is considered to be 0.05. Hence the critical probability value is p = 1 – (alpha / 2)

This probability value is given to be 0.975.

Now the degrees of freedom (d.f) = n – 1 = 50-1 = 49

The critical value is calculated to be 0.832.

Now the Margin of error; 0.832*5.91 = 4.92

Based on the mentioned values, the confidence interval can be written as follows;

(804.02 – 4.92, 804.92+4.92)

e) Rationalisation of the model

The rationale behind a model selection

Multiple linear regressions have been formed for the testing hypothesis purpose for assessing the impact of the years built and the land size on the impact sale price of the housing property. This can be thought of as the rationale behind the consideration of this particular model (Schönbrodt et al. 2017).

This section deals with the analysis of the model. This is based on the independent and dependent variables. Since the variable price is considered to change according to the market price, the sale prices of housing property in the Sydney market is assumed as the dependent variable.

Following these considerations, the independent variables are given as follows;

• Price Index in Sydney
• Years built
• Land size

Sale price = a +b1*Land size + b2*Price Index of property+b3*Year’s built+ u

In the above equation, b1, b2, and b3 are the coefficients of the dependent variable.

Units of measurement;

• Sale price- $ 000
• Land size – in square metres
• Built Years- in years

A sample size of 40 is considered for this model

f. Analysis of scatter plot

In this context, scatter plot can be analyzed by using DV and IVs.

Figure 2: Scatter plot of Market price 

(Source: Created by the researcher)

Figure 3: Scatter plot of Sydney price index

(Source: Created by the researcher)

Figure 4: Scatter plot of total number of square meters

(Source: Created by the researcher)

Figure 5: Scatter plot of ages of house (years)

(Source: Created by the researcher)

From the above graphs, it is possible to explain that values of the IVs and DVs are fluctuating at a rapid rate. In this regard, it has been found that the relationship between variables is showing   that market price is depends on the house ages, Sydney price index as well as square meter. As for this reason, it is possible to do market price analysis (Busk & Marascuilo, 2015).

g) Summary of the regression model

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.994165246
R Square	0.988364535
Adjusted R Square	0.987605701
Standard Error	4.655271329
Observations	50

Table 2: Summary Output

(Source: Created by Researcher)

ANOVA Table

[Refer to Excel]

From the above table, it can be viewed that the R square of this model has been estimated to be 0.988. Since the R square is close to 1, it represents the fact that this model is a good fit for the considered data set. It means the dependent variables can portray almost 98% of the variations in the chosen data set (List, Shaikh & Xu, 2019).

h) A Simple Linear regression model

Instead of the multiple linear regression models, this part deals with the simple linear regression model. The dependent variable is the market or the sale price, and land size is assumed as the independent or the explanatory variable.

The least sq. the regression equation is written in the following manner;

Market price = a + b1 * land size+ u.

In the equation, given above, the market price is the dependent variable and land size is the explanatory variable.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.993549238
R Square	0.987140089
Adjusted R Square	0.986872174
Standard Error	4.79104678
Observations	50

 Table 3: Summary Output

(Source: Created by Researcher)

 The R sq. for this model has been estimated to 0.98 which is close to 1. It depicts the fact that this model is suitable for the assessment of the impact of the chosen data.

	Coefficients
Intercept	410.2491857
Total number of square meters	1.756295916

Table 4: Coefficients

(Source: Created by Researcher)

With the increase in land size, the market price increases by 1.75 times the land size.

i) Interpretation of the slope coefficient

With the change in the independent variables, the slope of the regression line changes by 4.92 along with the average of the market price obtained to be 804.02. From the summary output, the slope is estimated to be 1.75.

j. Explanation of the coefficient determination

In this regard, it is possible to state the value of DV s and IVs with the help of statistical graph. The lane graph is described below with analysis:

 

Figure 6: Value of coefficient

(Source: Created by the researcher)

From the aforementioned graph, it is possible to explain that market price is dependent on the house age. The variables are dependent on each other. As for this reason, it is required to analyze the coefficient determination by using the value of the DV and IVs. .

k. Interpretation of the interval

In this regard, 95 percent level of confidence can be interpreted below:

t-Test: Paired Two Sample for Means
	Variable 1	Variable 2
Mean	804.023118	224.2070534
Variance	1748.509609	559.5661437
Observations	50	50
Pearson Correlation	#N/A
Hypothesized Mean Difference	0
df	49
t Stat	221.520716
P(T<=t) one-tail	1.68922E-75
t Critical one-tail	1.676550893
P(T<=t) two-tail	3.37844E-75
t Critical two-tail	2.009575199

Table 5: T-test

(Source: Created by the researcher)

From the above table, it has been detected that the mean value of total square value and market value are 224.2070534 and 804.023118 respectively. As for this reason, it is possible to say that the values are near to the unit value.

l) Comparison among the multiple regression model and simple linear regression model

Multiple regression model is actually a particular extension of simple linear regression and is used for predicting values of variable on the basis of other variables (Spokoiny & Dickhaus, 2015). On the other hand, simple linear regression is actually a model of linear regression having single explanatory variable. From the multiple linear regression model, it could be commented that, the observation value from summary output table is 50 whereas the observation value obtained for summary output for linear regression is also 50. It can be found that the significance value for ANOVA in multiple regression models is 1.781 and value for the same in the linear regression model is 4.82465360573579E-47. The standard errors values obtained from both the models signify that, the model needs rectification to become fit in the best possible way. From the residual output, it can be seen that, the standard residuals for observation 1 is -0.59 although the residuals for the 1^st observation is -0.76.

m) Prediction about the house prices

The market price for the house can be regarded as dependent variable and the total square meter is independent variable. The market price for the houses when the area is 250 sq km can be obtained from the provided formula below

Market price = a + b1 * land size+ u.

Here the value for a = 410.24 and on the other hand, b1 =1.756. Hence the market price is

410.24+1.756*250 = $849.24

From the calculated values an increase in the price of the houses can be observed with an increase in area of the houses.

n) Decision obtained from the hypothesis test

From the T test it could be said that land size ushers influence on the market price of the houses. Thus land area plays a great role in predicting the house prices.

o) Hypothesis formulation, statistical decision

• Alternative and null hypothesis

Null hypothesis (H0): Land size is highly useful for predicting the market price of any house

Alternative hypothesis (H1): Land size is not useful for predicting the market price of any house

• Statistical decision

It is possible to draw a statistical decision when the significant value is 5% for the Test. When the significant value is 5%, it could be said that, the null hypothesis is significant and acceptable.

• Conclusion

It can be commented from the above calculations and hypothesis, the Land size is highly useful for predicting the market price of any house (Bowers & Chen, 2019). Hence, it can be said that, null hypothesis can be accepted in the current context

Conclusion

It can be concluded that the price property of Sydney is calculated by using the values and data in an effective manner. In this context, it is possible to explain that the financial manager of the organization needs to focus on the sorted data. This assignment has dealt with the regression analysis along with the hypothesis formulation by using two samples T-test. Moreover, it has been identified that the market price is dependent on the Sydney price index along with a total number of square meters and age of houses.

 

References

Bowers, J., & Chen, N. (2019). Many tests, many strata: How should we use hypothesis tests to guide the next. Retrieved on 24^th November 2019 from: http://www.jakebowers.org/PAPERS/BowersChen2019Manytests.pdf

Busk, P. L., & Marascuilo, L. A. (2015). Statistical analysis in single-case research: Issues, procedures, and recommendations, with applications to multiple behaviors. In Single-Case Research Design and Analysis (Psychology Revivals) (pp. 171-198). Routledge. Retrieved on 14^th October 2019 from: https://www.researchgate.net/profile/T_Coburn/publication/227131127_Statistical_Methods_for_Spatial_Data_Analysis/links/5678d56708ae502c99d57e92/Statistical-Methods-for-Spatial-Data-Analysis.pdf

Komsta, L., & Novomestky, F. (2015). Moments, cumulants, skewness, kurtosis, and related tests. R package version, 14. Retrieved on 2^nd December 2019 from http://cran.ma.imperial.ac.uk/web/packages/moments/moments.pdf

Krause, F., & Rädler, K. H. (2016). Mean-field magnetohydrodynamics and dynamo theory. Elsevier. Retrieved on 1^st December 2019 fromhttps://books.google.com/books?hl=en&lr=&id=-504BQAAQBAJ&oi=fnd&pg=PP1&dq=Krause,+F.,+&+Rädler,+K.+H.+(2016).+Mean-field+magnetohydrodynamics+and+dynamo+theory.+Elsevier.+&ots=2WQkfxNiJw&sig=48dFmgWmx7Y8zSHrpn-mI165hrA

List, J. A., Shaikh, A. M., & Xu, Y. (2019). Multiple hypothesis testing in experimental economics. Experimental Economics, 22(4), 773-793. Retrieved on 26^th November 2019 from: https://cpb-us-w2.wpmucdn.com/voices.uchicago.edu/dist/f/1276/files/2018/09/3-mht-yar9iy.pdf

 Little, R. J., & Rubin, D. B. (2019). Statistical analysis with missing data (Vol. 793). John Wiley & Sons. Retrieved on 14^th October, 2019 from: https://leseprobe.buch.de/images-adb/61/97/61976bf3-cfac-463d-bb88-ca1ddb674cdf.pdf

Lugosi, G. (2018). Mean Estimation: Median of Means Tournaments. Retrieved on 3^rd December 2019 fromhttp://www.ub.edu/focm2017/slides/Lugosi.pdf

Schönbrodt, F. D., Wagenmakers, E. J., Zehetleitner, M., & Perugini, M. (2017). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences. Psychological methods, 22(2), 322. Retrieved on 26^th November 2019 from: https://osf.io/w3s3s/download?format=pdf

Spokoiny, V., & Dickhaus, T. (2015). Basics of modern mathematical statistics. Heidelberg: Springer. Retrieved on 24^th November 2019 from: http://premolab.ru/e_files/e279/IIp5B2cQ3B.pdf

 

 

 

Appendices

Appendix 1: Data set

Property Id	Market Price ($000)	Sydney price Index	Total number of square meters	Age of house (years)
19	912	144.0	287.8	4
25	885	116.5	277.3	6
36	877	118.0	272.0	13
42	874	94.8	269.1	17
51	863	63.2	259.2	11
58	860	132.5	253.3	10
69	846	132.5	248.1	35
72	846	101.7	246.4	29
80	842	113.4	242.9	39
85	839	117.6	241.6	19
87	839	171.0	241.1	34
92	837	136.3	239.2	22
93	836	110.3	239.2	3
101	833	79.3	236.0	23
102	833	111.5	235.8	34
107	831	98.0	234.6	24
111	829	84.2	234.4	40
115	827	99.0	233.8	28
121	824	92.2	232.2	1
128	820	110.8	230.3	3
149	806	63.5	224.7	22
150	805	126.1	224.5	2
151	805	149.0	224.1	9
154	803	83.1	223.1	20
157	799	108.0	222.8	11
163	796	108.1	221.2	13
170	792	45.5	219.6	8
179	789	85.5	216.4	16
181	788	129.0	215.6	13
182	788	38.6	215.6	45
184	787	78.0	215.1	30
191	781	111.1	213.4	8
192	780	167.6	212.9	5
194	780	90.2	212.8	3
201	777	97.0	211.0	7
203	776	130.6	209.7	21
204	776	127.2	209.6	18
210	773	107.2	208.7	23
222	770	135.6	204.0	24
233	763	81.3	201.4	25
241	759	70.6	199.3	23
242	759	59.2	198.5	42
249	754	82.1	196.3	3
250	754	164.9	196.1	20
254	752	95.3	195.5	9
259	749	110.0	193.9	33
261	748	107.4	193.6	31
269	747	141.2	192.9	14
270	746	87.0	192.6	41
272	745	99.4	191.3	0

(Source: Created by Researcher)