## 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 Table-4 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 Table-5 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 Table-5 shows, the p-value 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 p-value 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 Table-5 shows, the value of F-statistic for the model is 27.65 and the p-value 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.