Summary Statistics of House Prices in Kingfisher Bay

The city Kingfisher Bay is a conjured city within greater Melbourne and does not look like to any existing organisation or city. The city is consists of a number of various suburbs. Kingfisher Bay was constructed in various stages with new emerging suburbs. It involves some wealthy and some not so wealthy suburbs. The city is located on the bay. The city expands many kilometres along the beautiful beaches of bay and several kilometres inland. Almost sixty thousands people dwell in the suburbs of Kingfisher Bay.  

House prices in Kingfisher Bay:

The overall summary statistics of 120 house prices in Kingfisher Bay indicates that average of the price of house is $886.58 and middle value of the prices is $852. The difference of highest and lowest value of the price of houses is $1569 as the price of houses varies from $ 637.25 to $1081.75. 

The media articles focus on middle value of house prices and not the average. The cause is that, measure of middle value is more effective when sample size is big and does not involve outliers (the data that is not fitting according to the central tendencies of the distribution). Middle value stays in the middle of the dataset after orderly arrangement. The unfitted value of the central tendency does not also hamper the stability of Middle value. This dataset does not include unfitted value and the sample size is small. Besides, the average gives better approach of closeness of data values. Therefore, we must use the average for appropriate summary measure in this dataset, as it is more proper and less inconsistent measure of closeness of data values.

The proper measure of the average house price for all houses in Kingfisher Bay is within the interval of $828.43 to $944.72 with a significant level of validity.

The number of houses that sold for $1 million or more is 43. The proportion of such houses is 0.36. The proportion varies between 0.27 and 0.44 with a significant level of validity for the values of houses.

House prices vs. Conditions of suburbs in Kingfisher Bay:

Summary of conditions of houses: The frequency table and bar plot shows that most of the houses of Kingfisher Bay are either “Good” (frequency = 42) or “Poor” (frequency = 40) in condition. These two types of conditions of houses are followed by “Excellent” (frequency = 23). The lowest count of house condition is “Very poor” with frequency 15. The heights of bars in the bar plot are adjusted as per numbers of houses. 

Issues with Middle Value and Average as Summary Measures

Difference in means:

• We applied the testing procedure for examining equality of averages of levels of conditions of the houses among the suburbs in Kingfisher Bay. Our pre-assumed assertions are-

Basic assertion (H₀): The averages of levels of conditions of households are equal for all types of house conditions.

Alternative assertion (H_A): There exists at least one inequality of averages of levels of conditions of households for all types of house conditions.

The possibility of rejecting the basic assertion is 0.155998 that is greater than 0.05. Therefore, we accept the basic assertion of equality of averages of levels of conditions with a significant level of validity. We can say that the average levels of conditions of households are equal for all types of conditions of houses.

• We applied the testing procedure for examining the equality of average house prices of all house conditions in Kingfisher Bay. The pre-assumed assertions are-

Basic assertion (H₀): The averages of prices of conditions of households are equal for all types of house conditions.

Alternative assertion (H_A): There exists at least one inequality of averages of prices of conditions of households for every type of house conditions.

The possibility of rejecting is 0.000186 that is lesser than 0.05. Therefore, we reject the basic assertion of equality of averages of house prices of conditions of households with a significant level of validity. We can say that the average level of prices of conditions of households is equal for all types of house conditions.

• We applied the testing procedure for examining the equality of averages of house prices of all house suburbs in Kingfisher Bay. The pre-assumed assertions are-

Basic assertion (H₀): The averages of prices of conditions of households are equal for all types of house suburbs.

Alternative assertion (H_A): There exists at least one inequality of averages of prices of households’ conditions for all types of suburbs.

The possibility of rejecting is 0 that is lesser than 0.05. Therefore, we reject the basic assertion of equality of averages of house prices of households’ conditions with a significant level of validity. We can say that the average levels of prices of all house suburbs are equal.

From the so far analyses, we can decide that levels of conditions of different suburbs in Kingfisher Bay are equal. However, the prices of houses of different conditions and different suburbs are not equal to each other. From the completed analyses, we can determine that suburb or condition has a bigger influence on prices of houses. 

House prices vs. Condition of Suburbs in Kingfisher Bay:

Higher house prices have dependency on good rental investments:

We consider the house price as response or dependent variable and return of rent as single predictor or independent variable.

In this problem the linear regression model is-

Price$000 = 1300.51898 -111.425027*RentalReturn.

Hence, only 16.31% variability of house prices could be described by return of rent. The linear relationship of these two factors is negligible. The possibility of rejecting the significance of validity is (0.0) that is less than 0.05. According to the slope of dependent variable (a = -111.425027), we could state that RentalReturn is negatively related with Price$400. Hence, we can draw the conclusion that the rental return is unable to estimate house-prices. The fitted graph shows that the fitting is not also good.

Evaluation of Different Conditions and Suburbs of Houses

We supposed that good rental investments are looking for higher house prices. Hence, certainly our guess and concern of assumption of relevance of higher house prices with respect to good rental investments is not valid. The higher house prices driven by suburb or condition do not have a bigger impact on house prices.

Key Indicators of higher house prices:

The factors such as Age (-0.21782155), distance from buses (-0.02383229), distance from shops (-0.08373382), Kitchen (-0.0560762) and RentalReturn (-0.4038396) are negatively correlated. This means, when the values of these factors increase, then the values of price decrease.

The value of link of Price is moderately or highly positive with Rooms (0.505469281362907), Areasqm (0.567769140342605), Street (0.722570047931952), Storeys (0.565098454839622), Bedrooms (0.539744531398654), Bay Views (0.676193864685365) and WeeklyRent$ (0.665590917485361). Hence, these are the major factors for estimating prices of houses. These factors are the considerable indicators of higher prices. This means, when the values of these factors increase, then the values of price increase. These factors are the key indicators of the higher house prices.

Concerns developed by real estate agents and developers:

Weekly rent in Kingfisher Bay is at least $600

Suburb 1: According to the calculation, Suburb1 shows that the basic assertion of average of house prices is less than $600 is accepted. Therefore, the assumption of weekly rent of Kingfisher Bay at least $600 is false.

Suburb 2: According to the calculation, Suburb2 shows that the basic assertion of the average of house price is less than $600 are accepted. Hence, the assumption of weekly rent of Kingfisher Bay at least $600 is false.

Suburb 3: According to the calculation, Suburb3 indicates that the basic assumption of the average of house price is less than $600 is accepted. Hence, the assumption of weekly rent of Kingfisher Bay at least $600 is false. The average price is higher in case of Suburb3 of Kingfisher Bay.

For all the three suburbs, the assumption of weekly rent in Kingfisher Bay of being at least $600 is invalid.

At least 75% of houses are 10 years old or more:

According to the possibility of rejection region in this sample proportional table, we accept the basic assertion of proportional value less than 0.75. Hence, the assumption of age of 75% of houses 10 years and older is false at a significant level of validity.  

Future Surveys:

We are keen to compare house prices and rental availability. Specifically, the estimated average house price is less than $50000 and the true proportion of vacant houses in the market is within 3%.

The minimum sample size for calculating average is 163. The minimum sample size for proportion is 51. The table “Numerical Variable” of known standard deviation is considered for total size of the samples. With a high significant level of validity, the prices of house lie in the interval of $828.44 and $944.72. The table “Categorical Variable” of unknown proportional standard deviation shows the variation of prices of house of Suburb C indicates that there is a high chance of validity of proportions lying between 27.25% and 44.41%. The table of “Numerical Variable” when measure of deviation is known shows that measure of deviation are 244.717 and average of is 647.439 for the samples with sample size 41. The probability of rejection region shows that the assertion of mean house price less than $600 is rejected with a significant level of validity. The table of “Categorical Variable” when measure of deviation of proportion is unknown shows that among the sample size 120, we found the proportion of sample as 78.33% with standard error 3.76%. Therefore, we reject the basic assumption of average is less than 75% is rejected with a significant level of validity. 

Conclusion:

We may decide that most of the houses of Kingfisher Bay have Condition “Good”. The average prices of various Conditions and Suburbs are unequal. However, average Suburb levels in various Conditions have equality. The assumed assertion of average price is lesser than equal to $600 for all the three suburbs. The assumed average and proportion table indicates that the average house prices of all the suburbs is greater than or equal to 600 and proportion of age of houses greater than 10 years is more than 75%. The inter-relation among different estimators is described in this research analysis. You should not depend on rental investment for estimating house prices. You would also be concerned about the fact that more than 75% houses ages of the houses are older than 10 years.