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Descriptive Statistics and Relationships
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 Descriptive Statistics and Relationships
Descriptive Statistics and Relationships
Descriptive statistics involves organizing and summarizing data so that it can be understood easily. It provides basic information about the different variables available in a set of data and identifies potential relationships between variables. The most commonly used descriptive statistics today include measures of dispersion, measures of central tendency, shapes and distribution, and charts and graphs. By applying any of these, researchers can understand how data is distributed, which results in a better, more effective analysis.
Correlation
Variable 
Obs 
Mean 
Std. Dev. 
Min 
Max 
CV 
salesprice 
138 
1774282 
825409.5 
1000000 
4350000 
0.465208 
sqft 
138 
5691.297 
1694.75 
3099 
11704 
0.297779 
beds 
138 
4.543478 
1.004512 
3 
8 
0.221089 
baths 
138 
5.797101 
1.362476 
4 
11 
0.235027 
garage 
138 
3.731884 
1.645786 
2 
15 
0.441007 
pool 
138 
0.891304 
0.312391 
0 
1 
0.350488 
age 
138 
11.2971 
5.308593 
0 
26 
0.469908 
fireplaces 
138 
2.746377 
1.323905 
0 
7 
0.482055 
dom 
138 
105.8043 
110.8735 
0 
573 
1.047911 
summerlin 
138 
0.492754 
0.501769 
0 
1 
1.018295 
male 
138 
0.572464 
0.496523 
0 
1 
0.867344 
All the variables are numerical. While the variables pool, Summerlin, and males are categorical, all other variables are continuous.The average final sales price is $1,774,282 with a standard deviation of $825,409.5. Among the 11 variables, variable dom is maximum volatile as it has the highest coefficient of variation while, variable beds are least volatile as it has the lowest coefficient of variation. None of the variables has any missing values.

salesprice 
sqft 
beds 
baths 
garage 
pool 
age 
fireplaces 
dom 
Summerlin 
male 
salesprice 
1 










sqft 
0.6857 
1 









beds 
0.2939 
0.5814 
1 








baths 
0.5229 
0.782 
0.7425 
1 







garage 
0.3056 
0.5709 
0.3228 
0.5192 
1 






pool 
0.0861 
0.0586 
0.0501 
0.0164 
0.0287 
1 





age 
0.4238 
0.2146 
0.1359 
0.2691 
0.0551 
0.1693 
1 




fireplaces 
0.2788 
0.3763 
0.1922 
0.2343 
0.0959 
0.0035 
0.1012 
1 



dom 
0.0691 
0.1745 
0.0615 
0.0185 
0.0782 
0.0765 
0.1046 
0.0755 
1 


summerlin 
0.0912 
0.2845 
0.318 
0.2798 
0.0863 
0.168 
0.068 
0.0962 
0.0199 
1 

male 
0.0359 
0.0014 
0.118 
0.0219 
0.043 
0.0747 
0.0568 
0.044 
0.174 
0.0314 
1 
As the above table shows, all variables except the age of the property and males show an inverse relationship with the sales price. Sales price varies directly in the same direction with changes in other variables. Intuition also suggests that as facilities in a house increases, sales final price should also increase. Hence, our findings are consistent with the intuition.Price vs Sqft
Above Scatter plot and positive slope of fitted trendline shows that as size increases, sales price also increases (also suggested by the positive correlation coefficient)
a. Price vs Bath
Above Scatter plotand positive slope of fitted trendline shows that as no. of bathrooms increase, sales price also increases (also suggested by the positive correlation coefficient)
b. Price vs Age
Above Scatter plotand negative slope of fitted trendline shows that as age increases, sales price decreases (also suggested by the negative correlation coefficient)
c. Price vs DOM
Above Scatter plot and slightly positive slope of fitted trendlineshows that as age increases, sales price also slightly increases (also suggested by the very small positive correlation coefficient)
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Contrasting Characteristics of homes in Summerlin and in Henderson
Table 3: Descriptive Statistics (Average Values)
Variable 
Summerlin 
Henderson 
Price 
1850420 
1700320 
Sqft 
5203.838 
6164.829 
Bed 
4.220588 
4.857143 
Bath 
5.411765 
6.171429 
Garages 
3.588235 
3.871429 
Pool 
0.8382353 
0.9428571 
Age 
11.66176 
10.94286 
Fireplace 
2.617647 
2.871429 
DOM 
103.5735 
107.9714 
Agent_Gender 
0.5882353 
0.5571429 
As table 3 shows, the average sales price and the average age of the property for Summerlin is more as compared to Henderson. Similarly, in Summerlin, there are more no. of male agents as compared to Henderson. Apart from these variables, all other variables such as the average size of the houses, no. of bedrooms, bathrooms, garage space, pool, and fireplace availability and, average days the home was in the market for sale is more for Henderson as compared to Summerlin.Regression analysis
The average price of sold homes (breakdown by Location and Gender)

Female Agents 
Male Agents 
Summerlin 
2.00E+06 
1.70E+06 
Henderson 
1.60E+06 
1.80E+06 
Full 
1808444 
1748769 
As Table4 shows, in Summerlin, female agents significantly outperform male agents in terms of the sales price. While, in Henderson, male agents perform better than female agents. Overall, female agents outperform the male agents, which matches the findings of Josephine Fenton and Robert Villemaire.
Regression results
Table5:
a. As Table5 shows, as expected, variables sqft, baths, pool, fireplaces, Summerlin show a positive relationship with the sales price.While opposite to expected, variables beds, pool, and dom show a negative relationship with the sales price.And, as expected variables, age and males show a negative relationship with the sales price.
b. As the Table5 shows, the pvalue for the coefficients of variables sqft, pool, age, and Summerlin is <0.05. i.e. we can say with 95% confidence that the coefficients are statistically significant. While for all other variables, the pvalue is >0.05, hence, the null hypothesis (coefficient = 0) is not rejected and thus we can say that the coefficient is not statistically significant.
c. As Table5 shows, the value of Fstatistic for the model is 27.65 and the pvalue is 0.000 (<0.05). i.e. we can say with 95% confidence that the model statistically significantly fits the data. Also, R2 for the model is quite high (0.685). i.e. goodness of fit of the model is also very good.
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Conclusion
As the above analysis shows, sales value is statistically significantly affected by the size of the house, pool availability, age of the property, and if the property is Summerlin or Henderson. While Size, pool availability, and location show a positive relationship with sales value while the age of the property shows a negative relationship with sales value.i.e. the price of a new property is higher as compared to the old one. Similarly, Table4 shows, female listing agents produce greater returns as compared to males.