Regression Analysis for House Prices

This document provides an analysis of house prices using regression analysis. It explores the relationship between land size and house prices, and discusses the factors influencing house prices. The analysis reveals that land size alone is not enough to predict house prices, as other factors such as location, number of bedrooms, and economic conditions also play a significant role.

Research project
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Table of Contents
TASK 1........................................................................................................................................3
TASK 2........................................................................................................................................4
TASK 3........................................................................................................................................6
TASK 4........................................................................................................................................8
TASK 5........................................................................................................................................9
TASK 6......................................................................................................................................10
TASK 7......................................................................................................................................11
REFERENCES..............................................................................................................................13
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TASK 1
Land size
Column1
Mean 648.9
Standard Error 17.7227782
Median 639.5
Mode 970
Standard
Deviation 177.227782
Sample Variance 31409.6869
Kurtosis -0.7723054
Skewness 0.17931913
Range 646
Minimum 327
Maximum 973
Sum 64890
Count 100
Interpretation – It can be stated that mean of land size is 648.9 and median is 639.5. The SD is
177.2 and range is 646. So, land size of house is 650 m2.
House price
Column2
Mean 863.04
Standard Error 21.35328
Median 841.5
Mode 816
Standard
Deviation 213.5328
Sample Variance 45596.26
Kurtosis -0.81716
Skewness 0.196436
Range 789
Minimum 508
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Maximum 1297
Sum 86304
Count 100
Interpretation- From able it can be analysed that mean value is 863.04 and median is 841.5.
Moreover, the SD is 21.3 and range is 789. Thus, it is said price of house is average is $860
thousand.
TASK 2
Land size
Row Labels
Count of Land size
(m2)
300-399 16
400-499 7
500-599 22
600-699 26
700-799 10
800-899 9
900-1000 10
Grand Total 100
House price
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Row Labels
Count of Houses Price (thousand
$)
<600 4
600-699 16
700-799 18
800-899 14
900-999 19
1000-1099 16
1100-1199 6
1200-1300 7
Grand Total 100
Gender
Row Labels Count of Gender of Agent sold house
F 45
M 55
Grand Total 100
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TASK 3
Land size histogram
Bin Frequency
310 1
408.9 14
507.8 21
606.7 27
705.6 43
804.5 24
903.4 19
1002.3 11
1101.2 23
1200.1 10
More 7
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House price histogram
Bin Frequency
317 3
414.7 13
512.4 11
610.1 23
707.8 35
805.5 18
903.2 28
1000.9 33
1098.6 17
1196.3 8
More 11
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TASK 4
Mean and SD of house price and land size with male
Land size
Column1
Mean 745.6
Standard
Deviation 134.1225
House price
Column2
Mean 938.8727
Standard
Deviation 201.5427
Interpretation- It can be stated that mean of land size is 745.6 and SD is 134.1 whereas of mean
of house price is 938.8 ad SD is 201.5 in male gender.
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Mean and SD of house price with female
Land size
Mean 619.7684
Standard
Deviation 183.947
House price
Column2
Mean 874.5474
Standard
Deviation 188.5208
Interpretation- It can be stated that mean of land size is 619.7 and SD is 183.9 whereas of mean
of house price is 874.5 ad SD is 188.5 in male gender.
TASK 5
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.091288
R Square 0.008333
Adjusted R
Square -0.0119
Standard
Error 139.0594
Observations 51
ANOVA
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df SS MS F
Significance
F
Regression 1 7962.653 7962.653 0.411772 0.524062
Residual 49 947538.5 19337.52
Total 50 955501.2
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 809.3814 94.20615 8.591599 2.41E-11 620.0671 998.6958 620.0671 998.6958
X Variable 1 -0.06339 0.098784 -0.64169 0.524062 -0.2619 0.135125 -0.2619 0.135125
From above it can be infer that no male agents are not able to sell house having land size more
than 800 m2. Here, process followed is as follows :
 First is land size of house was identified whose land area was more than 800 m2. Then,
the agent gender (male) was determined who was involved in selling of house of that
particular area (Brook and Arnold 2018).
 Then, regression analysis was applied to find out significance value of male agent and
house sell. Thus, P value was identified that enabled in inferring the statement.
These steps were performed as it enabled in finding out confidence interval on 95%. Also, P
value was obtained from it. The answer can have change if house sold is 250 m2. This is because
SD of variable has changed. Hence, answer can be changed in this.
TASK 6
H0- There is no significance relationship between female agents and house with price high than
$ 700, 000
H1 – There is significance relationship between female agents and house with price high than
$700, 000
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One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
landsize 45 481.7111 119.50326 17.81449
houseprice 45 811.0889 154.63371 23.05143
One-Sample Test
Test Value = 700000
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the
Difference
Lower Upper
landsize -39266.807 44 .000 -699518.28889 -699554.1916 -699482.3861
houseprice -30331.691 44 .000 -699188.91111 -699235.3682 -699142.4540
Interpretation- It can be stated that significance value is P= .000 that is less than P= 0.05. thus,
here, null hypothesis is accepted. So, there is no significance relationship between female agents
and house with price high than $ 700, 000. The selling of house is does not depends on price.
There is change in decision between 1 and 10% level of significance. In this 1% is more
accurate as it interprets value related to 95%. But in 10% the value might not show accurate
outcomes.
In this as well same process was followed. The steps are:
 First is price of house was identified that was more than $700,000. Then, the agent
gender (female) was determined who was involved in selling of house of that particular
area (David 2017).
 Then, single sample t test was applied in which test value was changed and made to
$700,000.
TASK 7
Regression Statistics
Multiple R 0.127660833
R Square 0.016297288
Adjusted R
Square 0.006259505
Standard 147.8752818
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Error
Observations 100
ANOVA
df SS MS F
Significance
F
Regression 1 35503.3 35503.3 1.62359443 0.205604674
Residual 98 2142976 21867.1
Total 99 2178479
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 537.613365 66.55634 8.077567 1.7327E-12 405.5344647 669.6923 405.5345 669.6923
X Variable 1 0.098470466 0.07728 1.274203 0.20560467 -0.05488922 0.25183 -0.05489 0.25183
Interpretation- It can be analysed from table that the significance value obtained is P= .205
which is less than P= 0.05. This means that there is no relationship between land size and house
price. Thus, price of house is not related to its land size.
a) Linear regression=
y= bx+a+e
House price= b * land size +a.
b) Value of slope = 0.2158
c) Intercept of equation = 491.5723
d) It is evaluated that land size is not enough to predict house price. Besides, there are various
other factors as well which can be used to find house price (Quirk and Rhiney 2017). The
factors are location, number of bedroom, outdoor area, etc. in addition, price of house also
depends on interest rate, economic condition, income level of people, etc. Thus, these factors
also help is predicting house prices.
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REFERENCES
Books and journals
Brook, R.J. and Arnold, G.C., 2018. Applied regression analysis and experimental design. CRC
Press.
David, M., 2017. Statistics for managers, using Microsoft excel. Pearson Education India.
Quirk, T.J. and Rhiney, E., 2017. Excel 2016 for Advertising Statistics. Springer International
Publishing AG.
Daoud, J.I., 2017, December. Multicollinearity and regression analysis. In Journal of Physics:
Conference Series (Vol. 949, No. 1, p. 012009). IOP Publishing.
Brook and Arnold 2018
David 2017
Quirk and Rhiney 2017
Daoud 2017
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