The research has been conducted to understand the Housing Market. The variables taken into consideration are the cost of buying a particular house, the number of bedrooms the house consists, the type of house it is and the number of bathrooms in the house. The hometown’s postcode taken into consideration is B24 as the first part of the postcode to collect the data. So, on that particular area it can be understood that how much is the average prices of the house, number of bedroom and bathroom and which is most type of property type found in that location. Also, it can be compared what average that particular type of house has bedroom and washroom and the cost someone has to pay to buy the product. The source of the dataset is Properties For Sale in B24 | Rightmove. The total of 90 datasets has been taken for analysis consisting of various kinds of houses. The sampling method used for this analysis is clustered random sampling which is because from a particular pin code the data has been collected and the starting three element is B24 in this case. The problems and limitations in this dataset is that there are very less variables to decide which factors affect the cost of the house. Whether there is any relationship between cost and other independent factors like area location, quality of materials used, design type and other factors. Also, the dataset is from a particular pin code location for which it is difficult to come to a conclusion for all the locations other than the area selected. The same data is also very less so it is not much using for real time analysis with such less dataset.
Conducting Descriptive Statistics to understand the dataset.
|
Bedroom |
|
|
Mean |
3.53 |
|
Standard Error |
0.11 |
|
Median |
3.00 |
|
Mode |
3.00 |
|
Standard Deviation |
1.08 |
|
Sample Variance |
1.17 |
|
Kurtosis |
0.55 |
|
Skewness |
0.54 |
|
Range |
5.00 |
|
Minimum |
1.00 |
|
Maximum |
6.00 |
|
Sum |
318.00 |
|
Count |
90.00 |
|
Confidence Level (95.0%) |
0.23 |
The median value for bedroom variable data is found to be 3.00 with 95% confidence level. The median value is considered instead of mean because median does not consider the extreme values which can be all called as skewed value which reduces the statistical efficiency of the analysis. The skewness value is 0.54 which states that the data is slightly positively skewed as value is greater than 0.5. The maximum value is 6 and the minimum value is 1 (Nick 2007).
|
Washroom |
|
|
Mean |
1.48 |
|
Standard Error |
0.10 |
|
Median |
1.00 |
|
Mode |
1.00 |
|
Standard Deviation |
0.96 |
|
Sample Variance |
0.93 |
|
Kurtosis |
6.02 |
|
Skewness |
2.38 |
|
Range |
5.00 |
|
Minimum |
1.00 |
|
Maximum |
6.00 |
|
Sum |
133.00 |
|
Count |
90.00 |
|
Confidence Level (95.0%) |
0.20 |
The median value for bedroom variable data is found to be 1.00 with 95% confidence level. The median value is considered instead of mean because median does not consider the extreme values which can be all called as skewed value which reduces the statistical efficiency of the analysis. The skewness value is 2.38 which states that the data is slightly positively skewed as value is greater than 0.5. The maximum value is 6 and the minimum value is 1.
|
Cost |
|
|
Mean |
447354 |
|
Standard Error |
47615 |
|
Median |
350000 |
|
Mode |
375000 |
|
Standard Deviation |
451711 |
|
Sample Variance |
204043105697 |
|
Kurtosis |
44 |
|
Skewness |
6 |
|
Range |
3890000 |
|
Minimum |
110000 |
|
Maximum |
4000000 |
|
Sum |
40261896 |
|
Count |
90 |
|
Confidence Level (95.0%) |
94609 |
The median value for bedroom variable data is found to be 350,000 with 95% confidence level. The median value is considered instead of mean because median does not consider the extreme values which can be all called as skewed value which reduces the statistical efficiency of the analysis. The skewness value is 6 which states that the data is positively skewed as value is greater than 0.5. The maximum value is 4000000 and the minimum value is 110000.
|
Property_Type |
Count of Property_Type |
|
Apartment |
3 |
|
Bungalow |
2 |
|
Detached |
27 |
|
End of Terrace |
1 |
|
Flat |
1 |
|
Ground Flat |
1 |
|
House |
2 |
|
Maisonette |
1 |
|
Semi-Detached |
44 |
|
Terraced |
8 |
It is observed that the highest frequency is for Semi-Detached house which is 44 followed by Detached which is 27 and terraced which is 8. All other frequencies are very less with the sample data selected. So, it concludes that most of the frequency in B24 consists of semi-detached.
|
Property_Type |
Average Cost |
|
Apartment |
€ 130,000 |
|
Bungalow |
€ 250,000 |
|
Detached |
€ 764,630 |
|
End of Terrace |
€ 160,000 |
|
Flat |
€ 115,000 |
|
Ground Flat |
€ 140,000 |
|
House |
€ 287,500 |
|
Maisonette |
€ 110,000 |
|
Semi-Detached |
€ 357,432 |
|
Terraced |
€ 237,488 |
The average cost is found highest for Detached with € 764,630 followed by semi- detached with 357,432 euros. The lowest cost is found for maisonette with 110,000 euros. So, it can be interpreted that the cost of detached is very high in comparison to other houses. All the other types of houses have quite less average cost in comparison to detached houses.
The average bedrooms for each type of property
|
Property_Type |
Average of Bedroom |
|
Apartment |
1.7 |
|
Bungalow |
3.0 |
|
Detached |
4.1 |
|
End of Terrace |
2.0 |
|
Flat |
2.0 |
|
Ground Flat |
2.0 |
|
House |
5.0 |
|
Maisonette |
1.0 |
|
Semi-Detached |
3.5 |
|
Terraced |
3.4 |
The average number of bedrooms is found highest for house with 5 followed by detached with 4.1. The lowest average bedroom is found for maisonette being 1.
The average washrooms for each type of property
|
Row Labels |
Average of Washroom |
|
Apartment |
1.0 |
|
Bungalow |
1.0 |
|
Detached |
2.2 |
|
End of Terrace |
1.0 |
|
Flat |
1.0 |
|
Ground Flat |
1.0 |
|
House |
2.0 |
|
Maisonette |
1.0 |
|
Semi-Detached |
1.1 |
|
Terraced |
1.4 |
The average number of washrooms is found highest for detached with 2.2 followed by house with 2.0. All the other types of houses have average washroom of one.
Analyzing whether there is any relationship with cost of the house being a dependent variable and independent variables which are number of bedrooms and washrooms.
Hypothesis testing (Kruschke and Liddell 2018):
Hypothesis testing between cost and number of washrooms
H0: There is no significant relationship between cost and number of washrooms
H1: There is significant relationship between cost and number of washrooms
The p value is found to be 0.00 for 95% confidence level which means that null hypothesis is rejected and alternate hypothesis is accepted. Thus, it can be interpreted that there is significant relationship between cost of house and number of washrooms. The r squared value is found to be 0.40 which indicates that there is 40% of independent data represents the proportion of the variance for dependent variable which is considered weak or low effect.
Hypothesis testing between cost and number of bedrooms
H0: There is no significant relationship between cost and number of bedrooms
H1: There is significant relationship between cost and number of bedrooms
The p value is found to be 0.00 for 95% confidence level which means that null hypothesis is rejected and alternate hypothesis is accepted. Thus, it can be interpreted that there is significant relationship between cost of house and number of bedrooms. The r squared value is found to be 0.23 which indicates that there is 23% of independent data represents the proportion of the variance for dependent variable which is considered weak or low effect and much less than for washrooms.
Understanding whether different types of houses are in line with UK average price.
As found from the official website – office for National Statistics that the average price of houses in UK as of December, 2021 was 275000 euros. So, comparing 275000 with averages of each types of houses.
It is observed from the above chart that detached is almost three times the average house price in UK. Other than detached, semi -detached and house are only two types of houses which has average price greater than UK average price. Lowest average price is for maisonette and flat in comparison to average UK house price.
Correlation for washroom and bathroom with cost price of the house
Correlation between number of washroom and cost price of the house
|
Washroom |
Cost |
|
|
Washroom |
1 |
|
|
Cost |
0.630056519 |
1 |
Correlation coefficient has been used which explains that how strong is the relationship between the two variables. The correlation value between number of washrooms and cost of each house is 0.63 which indicates a strong positive correlation between these two variables as the value is greater than 0.5 (Ganti 2020).
Correlation between number of bedroom and cost price of the house
|
Cost |
Bedroom |
|
|
Cost |
1 |
|
|
Bedroom |
0.486812391 |
1 |
The correlation value between number of bedrooms and cost of each house is 0.48 which indicates a strong positive correlation between these two variables as the value is almost 0.5.
Regression equation to estimate the cost of a house all taken together in the region with cost being the dependent variable and number of bedrooms and washrooms being the independent variable.
The regression equation states that cost of a house (y) = (75565 * number of bedrooms) + (246133 * number of washrooms) -1833765. This is represented by y = m1x1 +m2x2 + c where y is the dependent variable, m1 and m2 are the slopes of bedroom and washroom respectively, x1 and x2 are the number of bedrooms and washrooms and c is the constant. So, putting the value of number of bedrooms and washrooms the value of cost can be found using the regression equation.
To understand heteroscedasticity of the error terms regression equation is conducted where residual square is the dependent variable and the independent variables are bedroom and washroom (Yang, K., Tu, J. and Chen, T., 2019).
H0: Error terms are homoscedasticity
H1: Error terms are heteroscedasticity
The significance F- value is found to be 0.003 which is less than 1. Thus, the null hypothesis is rejected and alternate hypothesis is accepted which means that the error terms are heteroscedasticity.
Again, to understand heteroscedasticity white test is conducted by conducting regression with residual square being y variable and predicted and predicted square being x variable.
H0: Error terms are homoscedasticity
H1: Error terms are heteroscedasticity
The significance F- value is found to be 0.003 which is less than 1. Thus, the null hypothesis is rejected and alternate hypothesis is accepted which means that the error terms are heteroscedasticity.
Conclusion
From the above analysis it is interpreted that the average cost is highest for Detached followed by semi- detached and lowest cost for maisonette. The average number of bedrooms is found highest for house with 5 followed by detached with 4.1. The lowest average bedroom is found for maisonette being 1. The average number of washrooms is found highest for detached with 2.2 followed by house with 2.0. All the other types of houses have average washroom of one. there is significant relationship between cost of house and number of washrooms. There is significant relationship between cost of house and number of bedrooms. It is observed from the above chart that detached is almost three times the average house price in UK. Other than detached, semi -detached and house are only two types of houses which has average price greater than UK average price. There is strong correlation for number of washrooms and bedrooms with cost of the house. So, it is interpreted that if the cost of the house is more it tends to have more washrooms and bedrooms.
References
Dataset Source- Properties For Sale in B24 | Rightmove
Ganti, A., 2020. Correlation coefficient. Corp. Financ. Account, 9, pp.145-152.
Kruschke, J.K. and Liddell, T.M., 2018. The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic bulletin & review, 25(1), pp.178-206.
Nick, T.G., 2007. Descriptive statistics. Topics in biostatistics, pp.33-52.
Yang, K., Tu, J. and Chen, T., 2019. Homoscedasticity: An overlooked critical assumption for linear regression. General psychiatry, 32(5).
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