Report on Housing Prices Statistics in Oregon from a Sample of 108 Houses Essay Example for Free

Report on Housing Prices Statistics in Oregon from a Sample of 108 Houses Essay From the eleven variables identified, area of living space in the house (sq_ft), age of the house in years (age) and selling price of the house in thousand dollars (price) were identified to be in the ratio scale for the level of measurement while number of bedrooms (beds), number of bathrooms (baths) and number of spaces for cars in the garage (garage) were identified to be in the ordinal. Lastly, the variables architectural style (style), school district were the house is located (school), method of heating the house (heat), presence of fireplace (fire) and presence of basement (basement) were identified to be in the nominal scale. These levels of measurement were the basis on what type of tests were done for the different analyses (See Appendices for table 1). On all the tests and comparisons with p-values, a 95% level of confidence is used. Descriptive Statistics on the Variables With the results gathered, most of the houses use the gas forced air method of heating. Out of the 108 houses, 96. 3% use this method while only 3. 7 use the electric baseboard heating. Also, most houses are of ranch architecture. Of the 108 houses, 40. 7% are of this architectural style, 36. 1% are of the tri-level style while 23. 1% are of the two-story type. Moreover, 84. 3% of the houses have basements. Similarly, 88. 9 of them have fireplaces. Lastly, the largest part sampled houses are located in the Apple Valley School District. From the 108 houses, 60. 2 are located in this school district while the rest are in Eastville (See Appendices for tables 2, 3, 4, 5 6). For the ordinal variables, the median number of bedrooms in the house is four which means that fifty percent of the houses have less than four bedrooms while the rest have more than four bedrooms. Similarly, fifty percent of the houses have less than three bathrooms while the other fifty percent have more than three bathrooms. In the number of spaces for cars in the garage, fifty percent of the houses can accommodate no more than two cars while the other fifty percent can. From the sample, most of the houses have three bedrooms, three bathrooms and can accommodate two cars. Since these three variables are rank variables, the means for each cannot be computed (See Appendices for tables 8, 9, 10 11). For the ratio variables, it was found out that the mean selling price of the house in Oregon is 97. 99226 thousand dollars. With a relatively small standard error of 2. 543183, the statistic for the selling price is considered accurate. Fifty percent of the houses are priced below 92. 46950 thousand dollars while the other 50% have selling prices greater than 92. 46950 thousand dollars. Having a variance of 698. 520, the data from the sample are considered to be extremely dispersed. On the average, the selling price of a house in Oregon deviates by 26. 429529 thousand dollars from the mean selling price of the house generated from the sample. The mean area of living space in the house in square feet is 1745. 72. However, the standard error of the mean, which is 42. 836, is sufficiently large. The data values for this variable are the most dispersed among the three ratio variables having a variance of 198173. 39. Fifty percent of the samples houses have areas which are below 1758. 00 square feet while the other fifty have areas greater than 1758. 00 square feet. On the average, the area of living space in the house deviates by 445. 167 square feet from the mean. For the last ratio variable, the mean age of the house in years is 11. 23. Having a standard error of 0. 448 which is very small, this statistic is considered accurate. Fifty percent of the sampled houses are below 11 years of age while the rest are more than 11 years of age. The distribution of the variable is not that dispersed. With a variance of 21. 675, the age variable is the least dispersed among the three ratio variables. On the average, the ages of the houses deviates from the mean by 4. 656 years only (See Appendices for table 13). Summing up the descriptive measures obtained on the eleven variables, a typical home in Oregon has an area of 1745. 72 square feet, approximately 11 years of age, has four bedrooms, three bathrooms and can accommodate two car spaces in the garage. Furthermore, it is of ranch architecture and uses the gas forced air method of heating. It has a basement and a fireplace. It is located in the Apple Valley School District and its selling price is 97. 99226 thousand dollars. Correlation From the scatterplots, the selling price is identified to have a positive linear relationship with area of living and a negative, close to nonlinear relationship with age of the house (See Appendices for figures 12 13). Since the data do not follow the normal distribution Spearman’s rho was used to determine the correlation between the dependent variable, price, and the other ratio scale variables (See Appendices for table 24). With a correlation coefficient of 0. 828, there is a positive very strong linear relationship between the selling price and area of living space in the house. Moreover, even if there is a negative weak linear relationship between selling price and age of the house in years, both the correlations of selling price with area and age are significant with p-value equal to 0. 000 (See Appendices for tables 14 15). Also, though there is a negative weak linear relationship between the ratio variables age and area for the -0. 292 Pearson correlation coefficient, the 0. 000 p-value says that the correlation is significant. Pearson correlation was used for the two ratio variables because both are normally distributed (See Appendices for table 22). For the ordinal variables, all of them have a significant correlation with selling price with p-values 0. 007, 0. 000 and 0. 000 for number of bedrooms, number of bathrooms and number of car spaces in garage, respectively. The number of bedrooms in the house has a positive weak linear relationship with selling price having a correlation coefficient of 0. 259. Moreover, the number of bathrooms in the house has a positive strong linear relationship with selling price having a correlation coefficient of 0. 675. Also, the number of spaces for cars in the garage has a positive moderate linear relationship with selling price having a correlation coefficient of 0. 475 (See Appendices for table 16). Among the ordinal variables, the number of bedrooms and number of bathrooms, and the number of car spaces and number of bathrooms has a significant correlation, with p-values equal to 0. 000 and 0. 003 respectively, and has a positive weak linear relationship, with correlation coefficients of 0. 358 and 0. 283 respectively (See Appendices for table 23). Among the nominal variables, only the architectural style has a positive moderate association with selling price having an Eta coefficient of 0. 485 (See Appendices for table 18). The rest has either weak or very weak associations with selling price (See Appendices for tables 17, 19, 20 21). For the two categories of method of heating, it was found out that the use of gas forced air in the house, presence of basement and presence of fireplace increases the selling price of the house. The school district location also affects the selling price. Houses located in Apple Valley School District tend to have higher prices than that of Eastville School District. Moreover, there are no significant differences on the selling prices of houses with tri-level and two-story architectural style. However, houses that are of ranch architectural style tend to have higher selling prices than that of the tri-level and two-story architectural styles (See Appendices for tables 31, 33, 35, 37, 39, 41 43). Predictors of Selling Price Using the regression model, the selling price of a house, when all other factors are held constant, decreases by 16. 113. The interpretation for the intercept is significant since the confidence interval of the estimate includes zero. Holding other factors constant, the selling price is estimated to increase by 0. 042 thousand dollars for every square feet increase in the area of living space of the house. Also, there is an estimated increase of 3. 269 thousand dollars on the selling price for every unit increase in the number of bedrooms holding other factors constant. The selling price is estimated to increase by 13. 876 thousand dollars for every unit increase in the number of spaces for cars in the garage holding other factors constant. Similarly, an increase of 6. 953 and 4. 269 thousand dollars on selling price is estimated if there is a basement and a fireplace, respectively, in the house. The selling price is also estimated to increase by 4. 874 thousand dollars if the house is located in Apple Valley School District with other factors held constant. Furthermore, the selling price is estimated to increase by 11. 053 thousand dollars if the house is of ranch architectural style holding other factors constant. If the house is of a two-story type, there is an estimated increase of 1. 714 thousand dollars. If the architectural style is tri-level, then the value to be multiplied with the beta estimates for two-story and ranch will be equal to zero since the coded value for tri-level in the dummy variables is zero (See Appendices for table 44). With a Durbin-Watson statistic of 1. 746, then the residuals are independent. Having an adjusted R square of 0. 820, the variation in the selling price of the house can be explained by the eleven variables. A mean square error of 126. 070 implies that the sum of the squared deviations of the selling prices to the true value is relatively small. With a computed F statistic of 45. 169 and a corresponding p-value of 0. 000, then the regression adequately represent the data and can be useful for prediction (See Appendices for tables 45 46). To test, given the following data on a certain house: two-story house with 1600 square feet, 3 bedrooms, 2 baths, a one car garage, gas heat, a basement, no fireplace, is 9 years old, and is in the preferred school district, then the predicted selling price of the house is 60. 804 thousand dollars. Summary The larger the area sizes of the living space of the house, the more expensive the selling price. Also, more number of bedrooms and spaces for car in the garage would also increase the selling price. In terms of architectural style, the ranch type would increase the selling price of a house most than the other two styles. Finally, the house with a basement, a fireplace and which is located in the Apple Valley School District increases also the selling price.