Quantitative Business Statistics

Quantitative Business Statistics

Memo:

To – Real Estate Developers

From – XYZ Cement Company

Subject: target area with high house value

XYZ cement company celebrates its 50 year in the cement business, our company offers superior and high quality cement to real estate developers, our company has faced high levels of competition but non of the upcoming firms can meet our standards, our plan is to help real estate development firms to realise their potentials by not only the sale of high quality cement at high discount rates but also to help these firms with information that will help them expand and also increase their revenue.

We have helped many firms realise their potential by giving them information which in turn results to the growth of the real estate industry. Our analysis on the various states where the median price of houses is high still remain undeveloped and we believe from the analysis of our data we believe that we can work together and benefit. We would like you to take into consideration the factors considered in this report and in turn we would like you to give us the responsibility of supplying cement to your construction sites.

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Introduction:

This paper reports on the various factors that influences house prices, some of the factors that we consider that influence price of houses included in this report are per capita income, population density, region or location, persons under the age of 18 years, persons aged above 25 years, foreign born persons and white persons born.

We consider income because the consumers disposable income determines the level of demand in almost all goods and services in the economy, we also consider the area west of Mississippi because we are convinced that this area the value of houses is higher than any other region, from our estimations therefore we will be able to show you the area which will result into more profits for your company.

All the factors above will influence the price of houses, after regressing the cost of houses as the dependent variable and the other variables as the independent variables, we will be in a position to estimate a model that can aid in the forecast of house prices, when the model is estimated and it has a strong predictive power then this model could be very useful in choosing where to construct new houses and increase revenue and returns due to high house prices.

Model:

We estimate the model using 8 variables, this include the median price of houses which is the dependent variable, the independent variables include percentage of white population, percentage of foreign born, percentage of bachelor degree, percentage persons under 18 years of age, per capita income, persons per square mile and the dummy variable which depict whether the region is west of Mississippi where if the value is one then the region is wet of Mississippi.

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We then assume that the letters represent the independent variables for easy calculation.

letter

Median value  of owner-occupied housing units, 2000

value

White  persons, percent, 2000 (a)

white

Foreign born  persons, percent, 2000

foreign

Bachelor’s  degree or higher, pct of persons age 25+, 2000

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bachelor

Persons under  18 years old, percent, 2000

P 18

Per capita  money income, 1999

income

Persons per  square mile, 2000

density

West of Mississippi

west

Therefore given the above assumptions then our estimated model will be stated as follows:

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Value = a + b1 white + b2 foreign + b3 bachelor + b4 P 18 + b5 income + b6 density + b7 west

Having stated our model the next step is to estimate the model using the linear classical regression model and at the same time checking the statistical significance of the parameters estimated.

Data:

The available data is from 50 regions both from west of Mississippi and those are not from the west of Mississippi, 30 regions are west of Mississippi and the other regions are not on the west of Mississippi, this sample will help us estimate our model due to the available data and various independent variables represented. The table below summarises the data and gives the values of means, mode, median and standard deviation of the data:

Table 1

total

mean

mode

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median

sd

Median value  of owner-occupied housing units, 2000

$6,743,800.00

$134,876.00

$0.00

$112,950.00

$82,945.18

White  persons, percent, 2000 (a)

2829%

57%

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68%

60%

16%

Foreign born  persons, percent, 2000

815%

16%

7%

14%

12%

Bachelor’s  degree or higher, pct of persons age 25+, 2000

1327%

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27%

19%

26%

8%

Persons under  18 years old, percent, 2000

1272%

25%

28%

26%

4%

Per capita  money income, 1999

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$1,034,044.00

$20,680.88

$0.00

$20,659.00

$4,058.83

Persons per  square mile, 2000

$255,966

5119.318

0

$3,472

4562.455577

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West of Mississippi

30

0.6

1

1

0.494871659

The mean percentage of population can be summarised by the diagram below:

An analysis of the mean of the value of houses in this region is presented below:

From the above chart therefore the mean value of houses in the two regions considerably has a large margin difference where the region west of Mississippi has a higher mean value of houses.

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Result:

After estimating our model which is

Value = a + b1 white + b2 foreign + b3 bachelor + b4 P 18 + b5 income + b6 density + b7 west, the model estimated took the following form:

Value =

-38821.8 -150324.3 white + 245105.96 foreign-134938.36 bachelor

-233659.1 P 18 + 14.11

506481

income +

0.375

density +

33636.89

west

From our estimated model we can describe it as follows, if we hold all other factors constant then the value of houses will be – 38821.8, if we hold all other factors constant and increase the percentage of white by one percent then the value will be reduced by 150324.3, if we hold all other factors constant and increase foreign by one percent then the value of houses will increase by 245105.96, further if bachelor degree level persons increase by one percent and we hold all other factors constant then the value of houses will reduce by 134938.

If the persons under 18 year of age increase by one percent and we hold all other factors constant then the value of houses will reduce by 233659, if income increase by one unit and we hold all other factors constant then the value of houses will increase by 14.115, if population

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density per square mile increase by one unit and we hold all other factors constant then the value of houses will increase by 0.375 and if the region in question is the west of Mississippi and we hold all other factors constant then the value of houses will increase by 33636.9.

The results of our estimated model can be presented in the diagram below:

Table 2

Coefficient

Conf. (±)

Std.Error

T

P

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Constant

-38821.80764

213885.0411

105981.9299

-0.366305913

0.715975656

White persons, percent, 2000 (a)

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-150324.305

81434.05176

40351.29303

-3.725390037

0.000575703

Foreign born persons, percent, 2000

245105.9586

132355.5996

65583.37046

3.737318728

0.000555629

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Bachelor’s degree or higher, pct of persons age 25+,  2000

-134938.358

361635.22

179193.4506

-0.753031752

0.455631272

Persons under 18 years old, percent, 2000

-233659.0981

538814.6561

266987.4285

-0.875168915

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0.386459544

Per capita money income, 1999

14.11506481

6.875247087

3.406745751

4.14326922

0.000161985

Persons per square mile, 2000

0.374580799

3.669981235

1.818508168

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0.205982467

0.837799834

West of                   Mississippi

33636.88136

28461.64901

14102.99886

2.385087149

0.021664451

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When we perform statistical tests at the 95% level then our null hypothesis will be as follows

value

standard error

T calculated T critical

null hypothesis

a

-38821.80764

105981.9299

-0.366306

1.95996

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accept

b1

-150324.305

40351.29303

-3.72539

1.95996

reject

b2

245105.9586

65583.37046

3.737319

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1.95996

reject

b3

-134938.358

179193.4506

-0.753032

1.95996

accept

b4

-233659.0981

266987.4285

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-0.875169

1.95996

accept

b5

14.11506481

3.406745751

4.143269

1.95996

reject

b6

0.374580799

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1.818508168

0.205982

1.95996

accept

b7

33636.88136

14102.99886

2.385087

1.95996

reject

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The null hypothesis states that the estimated parameter in question is equal to zero and the alternative hypothesis states that the parameter is not equal to zero, when we accept the null hypothesis then this means that the estimated parameter is not statistically significant, we accept the null hypothesis if the T calculated value is less than the t critical value and this test in our case is a two tail test meanings that we consider the negative and positive critical values.

After testing using the 95% levels then we reject the null hypothesis on the coefficients of foreign, bachelor, income, and west. By rejecting the null hypothesis then this means that they are statistically significant, we however accept the null hypothesis on the constant or the autonomous value, bachelor, persons under the age of 18 and population density per square mile.

When we reject the null hypothesis then this means that the parameter estimated is statistically significant, if we accept the null hypothesis then this means that the parameter is not statistically significant and therefore the model cannot be used for forecasting.

From our findings therefore it is clear that a region west of Mississippi has an added value in the value of houses, also that as the income levels of individuals increase then this will result into an increase in the value of houses. For this reason from our model therefore it would be more profitable to build in the area west of Mississippi which will result into higher levels of income.

Extension:

If we consider only the significant parameters and regress them then we will have the following

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results, this is done by stating the model as: Value = a + b1 foreign + b2 income + b6 density + b7 west,

Our estimated model will be as follows:

Value = -181992.4973 + 244196.8912 foreign + 12.07258088 income + 2.627983805 density + 23207.7848 west

Coefficient

Conf.  (±)

Std.Error

T

P

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Constant

-181992.4973

70038.39951

34773.00417

-5.233729489

4.20849E-06

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Foreign  born persons, percent, 2000

244196.8912

149401.8458

74175.7528

3.292139035

0.00194002

Per  capita money income, 1999

12.07258088

3.425039216

1.700480076

7.09951328

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7.25596E-09

Persons  per square mile, 2000

2.627983805

3.878036413

1.925386321

1.364912473

0.179066505

23207.7848

31499.22151

15638.88622

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1.483979388

0.14478555

According to our model our constant is negative 181992, the coefficient to the foreing born is positive, same case with that for income and density: when we test hypothesis for the significance of this value that we accept or reject the null hypothesis as follows:

Coefficient

T CALCULATED

T CRITICAL

NULL HYPOTHESIS

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Constant

-181992

-5.23373

1.95996

REJECT

Foreign born persons, percent, 2000

244196.9

3.292139

1.95996

REJECT

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Per capita money income, 1999

12.07258

7.099513

1.95996

REJECT

Persons per square mile, 2000

2.627984

1.364912

1.95996

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ACCEPT

West of

Mississippi

23207.78

1.483979

1.95996

ACCEPT

In our new model we find that our coefficients for foreign, income and our constant are

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Conclusion:

From our findings it is clear that if the areas west of Mississippi were developed then there would be an increase in the level of value of the houses, for this reason it would be profitable to invest in these area, another influential factor in the value of houses is the income level, when the level of income increase then the value of houses will increase. When we consider the increase in foreign citizens into the area then this has a positive result in the value of houses, when foreign residents increase then the value of houses also increase.

We therefore urge you to incest in the area west of Mississippi and as a result there will be increased value of investment, investing in this area will result into higher profits and we would like you to consider investing in this area and also that we would like to become partners in your venture by allowing us to supply cement into these areas.

References:

Burbidge S. (1993) Statistics: An Introduction to Quantitative Research,

McGraw Hill, New York

Kroenke D.(1997) Data Processing: Fundamental, Design and Implementation, Prentice Hall publishers, New York

Norman B. (2002) Analyzing Quantitative Data, sage publishers, New York

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House value data(2007) west Mississippi region house data,

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