# STATISTICS FOR FINANCIAL DECISIONS

Introduction. 2

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.

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]

## 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

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 1st 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 24th 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 14th 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 2nd 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 1st 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 Economics22(4), 773-793. Retrieved on 26th 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 14th 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 3rd 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 methods22(2), 322. Retrieved on 26th November 2019 from: https://osf.io/w3s3s/download?format=pdf

Spokoiny, V., & Dickhaus, T. (2015). Basics of modern mathematical statistics. Heidelberg: Springer. Retrieved on 24th 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)

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