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This is a solution of descriptive analysis visualization assignment help in which we discuss objective of carrying out exploratory, descriptive and regression analysis for gaining comprehensive understanding of house price in city
This report has been undertaken with the main objective of carrying out exploratory, descriptive and regression analysis for gaining comprehensive understanding of house price in the Shiraz region. It is also going to lay down understanding of most important factors that has been laying down impact over the housing prices in the area of Shiraz. The different analysis that has been carried out in this regard are as follows descriptive statistics, factors influencing house prices, development of multiple regression model and time series analysis.
Table 1: Descriptive statistics
Price($'000)
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Mean | 886.575 |
Standard Error | 29.66343575 |
Median | 852 |
Mode | 811 |
Standard Deviation | 324.9466579 |
Sample Variance | 105590.3305 |
Kurtosis | -0.14778497 |
Skewness | 0.426005063 |
Range | 1569 |
Minimum | 192 |
Maximum | 1761 |
Sum | 106389 |
Count | 120 |
From the above scatter diagram it could be interpreted that there is positive correlation between house price and area of the house in square meters as there is rightward movement and a straight line if drawn is going to originate out to high x- and y-values.
From the above scatter diagram it could be interpreted that there is positive correlation between house price and Street appeal as evaluated by the real estate agency as there is rightward movement and a straight line if drawn is going to originate out to high x- and y-values.
The above figure indicates that there is perfect positive linear relationship between the variables that are between house price and number of storey’s or levels in the house. It is because both the variables are moving towards the rightward direction and are seen to be away from each other.
Table 2: Correlation ship
| Price($'000) |
Price($'000) | 1 |
Rooms | 0.505469281 |
Street | 0.722570048 |
Storey’s | 0.565098455 |
Weekly Rent $ | 0.665590917 |
Bedrooms | 0.539744531 |
Bathrooms | 0.331222685 |
This model represents the independent variable that has been identified in order to present the dependent variable.
Y=α + βX1+BX2+BX3+BX4+BX5+ BX6…………..………………………. (Model 1)
Y= -386.984+ 0.174X1+0.212X2+89.86X3+188.42X4+106.80X5+-13.37X6
Dependent variable= Selling price of house in $'000
Independent variable= Rooms, Weekly rent, Street, Storey’s, Bedrooms and Bathrooms
Table 3: Multiple regression model 1
Regression Statistics
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Multiple R | 0.913271 |
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R Square | 0.834063 | |||||
Adjusted R Square | 0.825253 | |||||
Standard Error | 135.8368 | |||||
Observations | 120 | |||||
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ANOVA | ||||||
| df | SS | MS | F | Significance F |
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Regression | 6 | 10480214 | 1746702 | 94.66378 | 9.95E-42 |
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Residual | 113 | 2085036 | 18451.64 |
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Total | 119 | 12565249 |
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| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
Intercept | -386.984 | 102.3464 | -3.78111 | 0.000251 | -589.75 | -184.217 |
Rooms | 0.17444 | 25.05619 | 0.006962 | 0.994457 | -49.4664 | 49.81528 |
Weekly Rent $ | 0.212072 | 0.07814 | 2.714014 | 0.007689 | 0.057263 | 0.36688 |
Street | 89.8622 | 7.429578 | 12.0952 | 4.13E-22 | 75.14287 | 104.5815 |
Storey’s | 188.4243 | 26.93576 | 6.995319 | 1.98E-10 | 135.0597 | 241.7889 |
Bedrooms | 106.8086 | 31.44359 | 3.396831 | 0.000942 | 44.51315 | 169.104 |
Bathrooms | -13.3787 | 40.95154 | -0.3267 | 0.744502 | -94.5111 | 67.75365 |
R-Square
R-square value for the following model is 83.4%, indicates that 83.4% total variance in selling price of house in $'000 can be explained by independent variable Rooms, Weekly rent, Street, Storey’s, Bedrooms and Bathrooms
F-Value
The calculated F-value is greater than critical value of F thus it can be said that model is accepted. Even it can be said that value ration of explained to unexplained variance is seen to be very high. Hence, it can be said that regression variables are significant for explaining the dependent variable.
P-Value
Rooms, Street, Storey’s and Bathrooms have no influence on selling price of house in $'000 as it is not statistically significant because Rooms, Street, Storey’s and Bathrooms P-value is greater than 0.01% at 1% level of significance. On the other hand, weekly rent and bedrooms have influence on selling price of house in $'000 as it is statistically significant because weekly rent and bedrooms P-value is less than 0.01% at 1% level of significance.
Coefficients
Coefficient value indicates the rooms (0.17), weekly rent (0.21), street (89.8), storey’s (188.42) and bedrooms (106.8) have got dependability on selling price of house in $'000. In a case if Rooms, Weekly rent, Street, Storey’s and Bedrooms changes by one unit then selling price of house in $'000 will increase by 17%, 21%, 8900%, 18800% and 10600%. On the other hand, Bathrooms $ -13.37 have got no dependability on selling price of house in $'000. In a case if Bathrooms changes by one unit then selling price of house in $'000 will decrease by 1300%.
Linear regression model
This model represents the independent variable that has been identified in order to present the dependent variable.
Y=α + βX1+BX2+BX3…………..………………………. (Model 2)
Y= -409.72+ 97.7X1+200.19X2+127.61X3
Dependent variable= Selling price of house in $'000
Independent variable= Street, Storey’s and Bedrooms
Table 4: Multiple regression model 2
Regression Statistics
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Multiple R | 0.906903 |
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R Square | 0.822474 | |||||
Adjusted R Square | 0.817882 | |||||
Standard Error | 138.6718 | |||||
Observations | 120 | |||||
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ANOVA | ||||||
| df | SS | MS | F | Significance F |
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Regression | 3 | 10334586 | 3444862 | 179.1413 | 2.25E-43 |
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Residual | 116 | 2230663 | 19229.86 |
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Total | 119 | 12565249 |
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| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
Intercept | -409.729 | 58.34096 | -7.023 | 1.58E-10 | -525.28 | -294.177 |
Street | 97.711 | 7.009674 | 13.93945 | 1.52E-26 | 83.82745 | 111.5945 |
Storey’s | 200.197 | 27.0691 | 7.395776 | 2.39E-11 | 146.5833 | 253.8108 |
Bedrooms | 127.6109 | 11.84395 | 10.77435 | 3.52E-19 | 104.1525 | 151.0693 |
R-square value for the following model is 82.24%, indicates that 82.24% total variance in selling price of house in $'000 can be explained by independent variable Street, Storey’s, Bedrooms
F-Value
The calculated F-value is greater than critical value of F thus it can be said that model is accepted. Even it can be said that value ration of explained to unexplained variance is seen to be very high. Hence, it can be said that regression variables are significant for explaining the dependent variable.
P-Value
Street, Storey’s and Bedrooms have no influence on selling price of house in $'000 as it is not statistically significant because Street, Storey’s and Bedrooms P-value is greater than 0.01% at 1% level of significance.
Coefficients
Coefficient value indicates the street (97.71), storey’s (200.19) and bedrooms (127.61) have got dependability on selling price of house in $'000. In a case if Street, Storey’s and Bedrooms changes by one unit then selling price of house in $'000 will increase by 9700%, 20000%, and 12700%.
Linear regression model
This model represents the independent variable that has been identified in order to present the dependent variable.
Y=α + βX1+BX2+BX3…………..………………………. (Model 3)
Y= -60.14+ 97.7X1+317.87X2+137.10X3
Dependent variable= Selling price of house in $'000
Independent variable= Storey’s and Bedrooms
Table 5: Multiple regression model 3
Regression Statistics
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Multiple R | 0.724641 |
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R Square | 0.525104 | |||||
Adjusted R Square | 0.516986 | |||||
Standard Error | 225.8353 | |||||
Observations | 120 | |||||
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ANOVA | ||||||
| df | SS | MS | F | Significance F |
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Regression | 2 | 6598066 | 3299033 | 64.68494 | 1.21E-19 |
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Residual | 117 | 5967183 | 51001.56 |
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Total | 119 | 12565249 |
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| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
Intercept | -60.1449 | 85.78547 | -0.70111 | 0.484627 | -230.039 | 109.7487 |
Storeys | 317.8746 | 41.88497 | 7.589228 | 8.52E-12 | 234.9236 | 400.8255 |
Bedrooms | 137.1081 | 19.25664 | 7.120045 | 9.4E-11 | 98.97137 | 175.2449 |
R-square value for the following model is 52.5%, indicates that 52.5% total variance in selling price of house in $'000 can be explained by independent variable Storey’s and Bedrooms.
F-Value
The calculated F-value is greater than critical value of F thus it can be said that model is accepted. Even it can be said that value ration of explained to unexplained variance is seen to be very high. Hence, it can be said that regression variables are significant for explaining the dependent variable.
P-Value
Storey’s and Bedrooms have no influence on selling price of house in $'000 as it is not statistically significant because Storey’s and Bedrooms P-value is greater than 0.01% at 1% level of significance.
Coefficients
Coefficient value indicates the Storey’s (317.87) and bedrooms (137.10) have got dependability on selling price of house in $'000. In a case if Storey’s and Bedrooms changes by one unit then selling price of house in $'000 will increase by 31700% and 13700%.
Table 6: Mean absolute percentage error calculation
Time Period | Quarter | Median House Price ($'000) (A) | Forecasted (F) | Deviation(A-F) | Absolute deviation(/A-F/) | Absolute percentage of error=100(/A-F/)/ A |
1 | 2012-Q1 | 554 | 950 | -396 | 396 | 71 |
2 | 2012-Q2 | 589 | 1320 | -731 | 731 | 124 |
3 | 2012-Q3 | 661 | 1500 | -839 | 839 | 127 |
4 | 2012-Q4 | 522 | 1090 | -568 | 568 | 109 |
5 | 2013-Q1 | 610 | 950 | -340 | 340 | 56 |
6 | 2013-Q2 | 700 | 1320 | -620 | 620 | 89 |
7 | 2013-Q3 | 850 | 1500 | -650 | 650 | 76 |
8 | 2013-Q4 | 592 | 1090 | -498 | 498 | 84 |
9 | 2014-Q1 | 770 | 950 | -180 | 180 | 23 |
10 | 2014-Q2 | 880 | 1320 | -440 | 440 | 50 |
11 | 2014-Q3 | 1090 | 1500 | -410 | 410 | 38 |
12 | 2014-Q4 | 725 | 1090 | -365 | 365 | 50 |
13 | 2015-Q1 | 932 | 950 | -18 | 18 | 2 |
14 | 2015-Q2 | 1150 | 1320 | -170 | 170 | 15 |
15 | 2015-Q3 | 1330 | 1500 | -170 | 170 | 13 |
16 | 2015-Q4 | 940 | 1090 | -150 | 150 | 16 |
Total |
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| 943 |
A= actual valueWhere,
F= Forecasted value
n= Time period
From the above calculation of Mean absolute percentage error it could be interpreted that the measure of prediction accuracy of a forecasting value for Quarterly median house prices was seen to be around 58.9%. This shows price of the house vale at Shiraz to be accurate by 58.9%.
The present research proposal have been taken on the basis of appropriate variable for measuring the suitability of selling price of house in $'000 on the basis of various factors selected for carrying out the study. Further, if this analysis need to be repeated in the future then the various other factors that can be used for studying the suitability of Selling price of house in $'000 to be charged could be through inflation, personal disposable income, connectivity of city and location of Shiraz city at highway.
From the study it has been found that majority of the variables that has been laying down influence over the house price are Street, Storey’s and Bedrooms. This shows that Shiraz local government area must these independent variables to be important while carrying out their development process.