The price of houses varies due to various factors. Others might be very high mainly because of their locality and many other reasons, while others might be very low due to poor conditions of the houses or their sizes (Banerji, 2008). Objective of this report is to highlight factors that influence house pricing. To observe house prices distribution and the factors influencing it, the following data found in the internet detailing house prices in the Greater Manchester region will be analyzed statistically. It shows the locality, number of bedrooms, size of the garden, crime rate and price of the houses. Crime rate is categorized as very low, low, moderate and high.
Bedrooms
Size of the garden is the independent variable plotted on the X- axis. This is because the size of the garden does not depend on the price plotted on the Y- axis. Price of the garden depends on the size of the garden. According to the scatter diagram, the larger the garden size, number of bedrooms and low insecurity, the higher the price. The scatter diagram plotted above shows increasing house prices as the size of the garden increases.
Mean = Where x is the price of the houses and N is the sample size
Mean = 3,229,400 124,208 pounds. This represents the average house price.
Mode = 100,000 pounds. This represents the recurring house price.
Median = (100,000 + 100,000) 2 = 100,000 pounds. This represents the middle house price between the highest and lowest price recorded.
Range = highest observation – lowest observation = 360000 - 64000 = 296,000 pounds
Interquartile range (Q3 – Q1) is the difference between the upper quartile and the lower quartile,
Q1= 26/4th value = (85000+85500)/2= 85,250 pounds
Q3= 26*3/4 value = (129950+130000)/2= 129,975 pounds
Interquartile range = 129975 - 85250 = 44,725 pounds
Price in Pounds (Y)
‘000’
Size of garden (X) ‘000’
Correlation Coefficient
r = ss xy ÷ r = 516.43 ÷
= 516.43/742.2 r = 0.70
Comment: Strong positive correlation between the size of the house and its selling price.
The positive correlation coefficient proves there is a linear relationship between the size of the house and the selling price.
Regression Equation
Equation of regression is given by; Y= a + b x
Where b is the gradient, x is the independent variable used to predict y, a is y-intercept and y is the dependent variable that the equation tries to predict.
Normal equations:
1.91*(3229.4=26bo + 49.58b1)
6674.65=49.58bo + 99.51b1
Therefore, 6158.22= 49.58bo+94.70b1
6674.65=49.58bo+99.51b1
516.43= 4.81 b1 b1=516.43÷ 4.81 = 107.37
26bo= 3229.4– (49.58*b1)
26bo= 3229.4- (5323.4)
bo= -80.54
Regression equation of Y on X:
Y=107.37x – 80.54
Regression equation estimates the selling price of a house given its size in sq ft. X represents the size of the house.
Standard deviation
Variance,
Mean X= 49.58/26= 1.91
Mean Y= 3229.4/26= 124.21
N – 1= 26 – 1=25
∑= 5.0054
X represents price while µ(X bar) represents the mean for the prices.
Summation = 5.0054 Variance = 5.0054÷ (26-1) = 0.2
Standard Deviation = square root variance = 0.45%
Standard deviation represents the extent of deviation of the garden size in percentage.
According to various secondary sources, prices for houses in UK have varied over a long period. Data used is from March 2002 to March 2012, where we realize that in March 2007 house price was at its peak and in 2002 at its lowest point over the stipulated period. The following graph shows how the average house prices have changed over the past few years. A price index is made from it using the following formula:
(Y/x) 100%;
Y is the value of the year you want to calculate for while x is the average of the previous year.
Recently the average house price in Canada rose to £236,610, which is slightly higher than the average house prices around the Greater Manchester region. This might be due to the size of the garden, which directly influences the price of the house. Housing units in Canada have bigger garden sizes compared to those in the UK.
CONCLUSION
A variety of factors determines how a house costs. Factors like, crime rate heavily affect the price of many houses. With areas that have very low levels of crime rate being sold at higher prices and those with high level being sold at a lower price. In addition, the number of bedrooms also affects the price of the house. This is realised when all the other variables are kept constant. When all the variables are put together, the value of the house is determined. For a house to be highly priced, all the variables must be at their best.
Reference list
Banerji, A. (2008). House price developments in Europe: a comparison. Washington, DC: IMF)
Crawley, M. J. (2011). An introduction using R. Hoboken: John Wiley & Sons.
Die wert, W.E. (2009). Price index concepts and measurement. Chicago: University of Chicago Press
Gravette, F. J. (2011). Essentials of statistics for the behavioral sciences. Belmont, CA : Wadsworth
Lambert, S. (2012). What next for house prices? This is money. Retrieved May 20, 2012, from http://www.thisismoney.co.uk/money/mortgageshome/article-1671748/House-prices-What-expect--news-predictions.html.
Moore, D. S (1997). Statistics: Concepts and Controversies. New York: W. H. Freeman and Company
Spiegel, M. R. (1999). Schaum's outline of theory and problems of statistics. New York, NY [u.a.]: McGraw-Hill
Tsounta, E. (2009). Is the Canadian housing market overvalued? : A post-crisis assessment. Washington, D.C: International Monetary Fund.
