Price predection of houses

datadictonary

price represents the sale price of a house in Rs. area gives the total size of a property in square feet bedrooms represents the number of bedrooms bathrooms shows the number of bathrooms stories variable shows the number of stories excluding basement mainroad =1 if the house faces a main road livingroom = 1 if the house has a separate living room or a drawing room for guests basement shows if the house has a basement hotwaterheating = 1 if the house uses gas for hot water heating airconditioning = 1 if there is central air conditioning parking shoes the number of cars that can be parked prefarea is 1 if the house is located in the preferred neighbourhood of the city

data <- read.csv('file:///C:/Users/badal/Desktop/datset_/usecase/Housing.csv')
head(data)

any(is.na(data))

[1] FALSE

str(data)

'data.frame':   545 obs. of  13 variables:
 $ price           : int  13300000 12250000 12250000 12215000 11410000 10850000 10150000 10150000 9870000 9800000 ...
 $ area            : int  7420 8960 9960 7500 7420 7500 8580 16200 8100 5750 ...
 $ bedrooms        : int  4 4 3 4 4 3 4 5 4 3 ...
 $ bathrooms       : int  2 4 2 2 1 3 3 3 1 2 ...
 $ stories         : int  3 4 2 2 2 1 4 2 2 4 ...
 $ mainroad        : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
 $ guestroom       : Factor w/ 2 levels "no","yes": 1 1 1 1 2 1 1 1 2 2 ...
 $ basement        : Factor w/ 2 levels "no","yes": 1 1 2 2 2 2 1 1 2 1 ...
 $ hotwaterheating : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ airconditioning : Factor w/ 2 levels "no","yes": 2 2 1 2 2 2 2 1 2 2 ...
 $ parking         : int  2 3 2 3 2 2 2 0 2 1 ...
 $ prefarea        : Factor w/ 2 levels "no","yes": 2 1 2 2 1 2 2 1 2 2 ...
 $ furnishingstatus: Factor w/ 3 levels "furnished","semi-furnished",..: 1 1 2 1 1 2 2 3 1 3 ...

library(dplyr)

data$mainroad <-factor(data$mainroad, labels = c("No","Yes"))
data$guestroom <-factor(data$guestroom, labels = c("No","Yes"))
data$basement <-factor(data$basement, labels = c("No","Yes"))
data$hotwaterheating <-factor(data$hotwaterheating, labels = c("No","Yes"))
data$airconditioning <-factor(data$airconditioning, labels = c("No","Yes"))
data$parking <- factor(data$parking, labels = c("No","Small","Medium", "Large"))
data$prefarea<- factor(data$prefarea,labels = c("No","Yes"))
data$furnishingstatus<- factor(data$furnishingstatus, labels =c("furnished", "semi-furnished", "unfurnished"))

summary(factor(data$furnishingstatus))

     furnished semi-furnished    unfurnished 
           140            227            178 

fst <- data.frame(model.matrix( ~ furnishingstatus, data))
fst

fst <- fst[,-1]
data<- cbind(data[,-13], fst)

summary(data)

     price               area          bedrooms       bathrooms        stories      mainroad  guestroom basement  hotwaterheating airconditioning   parking    prefarea 
 Min.   : 1750000   Min.   : 1650   Min.   :1.000   Min.   :1.000   Min.   :1.000   No : 77   No :448   No :354   No :520         No :373         No    :299   No :417  
 1st Qu.: 3430000   1st Qu.: 3600   1st Qu.:2.000   1st Qu.:1.000   1st Qu.:1.000   Yes:468   Yes: 97   Yes:191   Yes: 25         Yes:172         Small :126   Yes:128  
 Median : 4340000   Median : 4600   Median :3.000   Median :1.000   Median :2.000                                                                 Medium:108            
 Mean   : 4766729   Mean   : 5151   Mean   :2.965   Mean   :1.286   Mean   :1.806                                                                 Large : 12            
 3rd Qu.: 5740000   3rd Qu.: 6360   3rd Qu.:3.000   3rd Qu.:2.000   3rd Qu.:2.000                                                                                       
 Max.   :13300000   Max.   :16200   Max.   :6.000   Max.   :4.000   Max.   :4.000                                                                                       
 furnishingstatussemi.furnished furnishingstatusunfurnished
 Min.   :0.0000                 Min.   :0.0000             
 1st Qu.:0.0000                 1st Qu.:0.0000             
 Median :0.0000                 Median :0.0000             
 Mean   :0.4165                 Mean   :0.3266             
 3rd Qu.:1.0000                 3rd Qu.:1.0000             
 Max.   :1.0000                 Max.   :1.0000             

library(ggplot2)
ggplot(data, aes(x=price))+ geom_histogram(bins = 30)

ggplot(data, aes(x= price))+geom_histogram(bins = 30, fill= "blue", col= "red")

ggplot(data, aes(y= price, x= hotwaterheating, fill= hotwaterheating))+ geom_boxplot()

ggplot(data, aes(y= price, x= airconditioning, fill= airconditioning))+ geom_boxplot()

ggplot(data, aes(x= area, y= price))+ geom_point(col="red")+geom_smooth(method = 'lm', se=F)

ggplot(data, aes(x= area, y= price, col=factor(bedrooms)))+ geom_point(col="lightblue")+geom_smooth(method = 'lm', se=F)+labs(col="bedrooms")

# Let us create the new metric and assign it to "areaperbedroom"
data$areaperbedroom <- data$area/data$bedrooms
# metric - bathrooms per bedroom
data$bbratio <- data$bathrooms/data$bedrooms

splitting data

library(caTools)
set.seed(123)
index<- sample.split(data$price,SplitRatio = 0.65)
train <- subset(data,index==T)
test<- subset(data,index==F)

nrow(train)

[1] 385

nrow(test)

[1] 160

model bulding

model1<- lm(Formula=price~.,data=train) #selecting all variables. 

In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
 extra argument 㤼㸱Formula㤼㸲 will be disregarded

summary(model1)

Call:
lm(data = train, Formula = price ~ .)

Residuals:
     Min       1Q   Median       3Q      Max 
-2504113  -634879   -80599   511075  5060460 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)                      874315.2   848433.8   1.031 0.303452    
area                                360.8      105.8   3.410 0.000722 ***
bedrooms                        -211715.4   249807.2  -0.848 0.397260    
bathrooms                       1398493.1   558261.1   2.505 0.012675 *  
stories                          415843.4    79577.0   5.226 2.92e-07 ***
mainroadYes                      560392.0   180753.6   3.100 0.002083 ** 
guestroomYes                     434052.3   163788.7   2.650 0.008396 ** 
basementYes                      241724.3   137721.0   1.755 0.080064 .  
hotwaterheatingYes               780537.4   268829.4   2.903 0.003914 ** 
airconditioningYes               874359.9   135570.6   6.449 3.54e-10 ***
parkingSmall                     457162.3   145060.5   3.152 0.001758 ** 
parkingMedium                    590082.4   164977.0   3.577 0.000394 ***
parkingLarge                     314956.0   466080.5   0.676 0.499622    
prefareaYes                      684629.3   142398.9   4.808 2.23e-06 ***
furnishingstatussemi.furnished    48379.0   147553.0   0.328 0.743193    
furnishingstatusunfurnished     -323248.4   158810.0  -2.035 0.042525 *  
areaperbedroom                     -381.2      286.5  -1.330 0.184208    
bbratio                        -1024676.6  1704794.7  -0.601 0.548174    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1108000 on 367 degrees of freedom
Multiple R-squared:  0.6846,    Adjusted R-squared:   0.67 
F-statistic: 46.85 on 17 and 367 DF,  p-value: < 2.2e-16

For the calculation of VIF you need to install the package “car”,

First let’s install this package in your R system

install.packages(“car”)

# Pass the model_1 in the vif function
library(car)
vif(model1)

                      GVIF Df GVIF^(1/(2*Df))
area             16.023437  1        4.002928
bedrooms         10.515692  1        3.242791
bathrooms        23.322562  1        4.829344
stories           1.572269  1        1.253901
mainroad          1.177956  1        1.085337
guestroom         1.252031  1        1.118942
basement          1.372742  1        1.171641
hotwaterheating   1.063719  1        1.031367
airconditioning   1.269521  1        1.126730
parking           1.318628  3        1.047178
prefarea          1.182424  1        1.087393
furnishingstatus  1.167263  2        1.039423
areaperbedroom   17.814876  1        4.220767
bbratio          22.452484  1        4.738405

model2 <- lm(formula = price ~ area + bedrooms + bathrooms + stories + mainroad + guestroom + 
                basement + hotwaterheating + airconditioning + parking + prefarea + 
                furnishingstatusunfurnished + furnishingstatussemi.furnished + areaperbedroom, data = train)
summary(model2)

Call:
lm(formula = price ~ area + bedrooms + bathrooms + stories + 
    mainroad + guestroom + basement + hotwaterheating + airconditioning + 
    parking + prefarea + furnishingstatusunfurnished + furnishingstatussemi.furnished + 
    areaperbedroom, data = train)

Residuals:
     Min       1Q   Median       3Q      Max 
-2550916  -638396   -98127   516615  5072424 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)                     504181.15  583121.69   0.865 0.387808    
area                               382.71      99.29   3.854 0.000137 ***
bedrooms                       -100804.09  168237.94  -0.599 0.549424    
bathrooms                      1072508.43  132203.38   8.113 7.48e-15 ***
stories                         414366.54   79470.03   5.214 3.09e-07 ***
mainroadYes                     558913.32  180579.95   3.095 0.002118 ** 
guestroomYes                    435813.52  163620.33   2.664 0.008072 ** 
basementYes                     232302.09  136707.18   1.699 0.090114 .  
hotwaterheatingYes              793375.52  267746.91   2.963 0.003243 ** 
airconditioningYes              876153.64  135420.09   6.470 3.13e-10 ***
parkingSmall                    454774.39  144880.17   3.139 0.001832 ** 
parkingMedium                   586211.81  164708.19   3.559 0.000421 ***
parkingLarge                    313365.81  465668.30   0.673 0.501409    
prefareaYes                     694044.67  141411.80   4.908 1.39e-06 ***
furnishingstatusunfurnished    -319135.12  158524.78  -2.013 0.044826 *  
furnishingstatussemi.furnished   52813.02  147240.55   0.359 0.720036    
areaperbedroom                    -440.19     268.90  -1.637 0.102490    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1107000 on 368 degrees of freedom
Multiple R-squared:  0.6843,    Adjusted R-squared:  0.6705 
F-statistic: 49.85 on 16 and 368 DF,  p-value: < 2.2e-16

vif(model2)

                                    GVIF Df GVIF^(1/(2*Df))
area                           14.130284  1        3.759027
bedrooms                        4.777825  1        2.185824
bathrooms                       1.310211  1        1.144644
stories                         1.570770  1        1.253303
mainroad                        1.177738  1        1.085236
guestroom                       1.251630  1        1.118763
basement                        1.354957  1        1.164026
hotwaterheating                 1.057004  1        1.028107
airconditioning                 1.268906  1        1.126457
parking                         1.316335  3        1.046874
prefarea                        1.168115  1        1.080794
furnishingstatusunfurnished     1.738832  1        1.318648
furnishingstatussemi.furnished  1.660610  1        1.288647
areaperbedroom                 15.721413  1        3.965024

model3 <- lm(formula = price ~ area + bathrooms + stories + mainroad + guestroom + 
                basement + hotwaterheating + airconditioning + parking + prefarea + 
                furnishingstatusunfurnished , data = train)
summary(model3)

Call:
lm(formula = price ~ area + bathrooms + stories + mainroad + 
    guestroom + basement + hotwaterheating + airconditioning + 
    parking + prefarea + furnishingstatusunfurnished, data = train)

Residuals:
     Min       1Q   Median       3Q      Max 
-2717894  -697257   -82137   520522  5133541 

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   67407.81  258253.68   0.261 0.794227    
area                            230.66      31.05   7.429 7.62e-13 ***
bathrooms                   1117247.71  130199.08   8.581 2.61e-16 ***
stories                      473118.95   74185.73   6.377 5.36e-10 ***
mainroadYes                  513703.01  179125.33   2.868 0.004369 ** 
guestroomYes                 453188.36  163358.83   2.774 0.005814 ** 
basementYes                  263532.17  135836.00   1.940 0.053128 .  
hotwaterheatingYes           839534.98  266952.44   3.145 0.001796 ** 
airconditioningYes           872528.97  134318.11   6.496 2.66e-10 ***
parkingSmall                 452148.84  144948.03   3.119 0.001954 ** 
parkingMedium                633548.13  163661.27   3.871 0.000128 ***
parkingLarge                 326493.45  466152.48   0.700 0.484116    
prefareaYes                  713937.40  141381.32   5.050 6.95e-07 ***
furnishingstatusunfurnished -353514.59  125478.26  -2.817 0.005101 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1110000 on 371 degrees of freedom
Multiple R-squared:  0.6799,    Adjusted R-squared:  0.6687 
F-statistic: 60.61 on 13 and 371 DF,  p-value: < 2.2e-16

vif(model3)

                                GVIF Df GVIF^(1/(2*Df))
area                        1.373955  1        1.172158
bathrooms                   1.263554  1        1.124079
stories                     1.361032  1        1.166633
mainroad                    1.152246  1        1.073427
guestroom                   1.240534  1        1.113792
basement                    1.330131  1        1.153313
hotwaterheating             1.044762  1        1.022136
airconditioning             1.241236  1        1.114108
parking                     1.279746  3        1.041967
prefarea                    1.160968  1        1.077482
furnishingstatusunfurnished 1.083233  1        1.040785

model4 <- lm(formula = price ~ area + bathrooms + stories + guestroom  + hotwaterheating + airconditioning + parking + prefarea + 
                furnishingstatusunfurnished , data = train)
summary(model4)

Call:
lm(formula = price ~ area + bathrooms + stories + guestroom + 
    hotwaterheating + airconditioning + parking + prefarea + 
    furnishingstatusunfurnished, data = train)

Residuals:
     Min       1Q   Median       3Q      Max 
-2470160  -705623   -65999   542942  4978397 

Coefficients:
                             Estimate Std. Error t value Pr(>|t|)    
(Intercept)                  524701.2   226280.8   2.319 0.020945 *  
area                            240.5       30.6   7.861 4.14e-14 ***
bathrooms                   1122153.8   130017.8   8.631  < 2e-16 ***
stories                      464459.9    72257.6   6.428 3.96e-10 ***
guestroomYes                 592026.6   154061.0   3.843 0.000143 ***
hotwaterheatingYes           828926.7   270674.9   3.062 0.002355 ** 
airconditioningYes           885373.1   135998.4   6.510 2.43e-10 ***
parkingSmall                 420311.3   146567.5   2.868 0.004370 ** 
parkingMedium                680754.2   164628.6   4.135 4.39e-05 ***
parkingLarge                 343451.2   472485.0   0.727 0.467741    
prefareaYes                  808448.2   140061.2   5.772 1.65e-08 ***
furnishingstatusunfurnished -389529.7   126695.6  -3.075 0.002264 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1126000 on 373 degrees of freedom
Multiple R-squared:  0.6691,    Adjusted R-squared:  0.6593 
F-statistic: 68.55 on 11 and 373 DF,  p-value: < 2.2e-16

vif(model4)

model5 <- lm(formula = price ~ area + bathrooms + stories + guestroom  + airconditioning + parking + prefarea + 
                furnishingstatusunfurnished , data = train)
summary(model5)

Call:
lm(formula = price ~ area + bathrooms + stories + guestroom + 
    airconditioning + parking + prefarea + furnishingstatusunfurnished, 
    data = train)

Residuals:
     Min       1Q   Median       3Q      Max 
-2492575  -726320   -59881   537245  4937129 

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                  547793.05  228674.29   2.396 0.017088 *  
area                            237.67      30.92   7.686 1.35e-13 ***
bathrooms                   1152405.25  131086.12   8.791  < 2e-16 ***
stories                      470095.47   73038.79   6.436 3.76e-10 ***
guestroomYes                 606471.32  155704.11   3.895 0.000116 ***
airconditioningYes           822323.40  135928.50   6.050 3.52e-09 ***
parkingSmall                 434164.62  148129.56   2.931 0.003587 ** 
parkingMedium                724408.27  165837.22   4.368 1.62e-05 ***
parkingLarge                 329687.82  477726.52   0.690 0.490548    
prefareaYes                  789730.13  141486.46   5.582 4.58e-08 ***
furnishingstatusunfurnished -407778.37  127965.13  -3.187 0.001560 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1138000 on 374 degrees of freedom
Multiple R-squared:  0.6607,    Adjusted R-squared:  0.6517 
F-statistic: 72.84 on 10 and 374 DF,  p-value: < 2.2e-16

vif(model5)

                                GVIF Df GVIF^(1/(2*Df))
area                        1.296377  1        1.138585
bathrooms                   1.218382  1        1.103803
stories                     1.254952  1        1.120246
guestroom                   1.072052  1        1.035399
airconditioning             1.209201  1        1.099637
parking                     1.237144  3        1.036104
prefarea                    1.106008  1        1.051669
furnishingstatusunfurnished 1.071669  1        1.035214

head(price_pred,10)

       1        3        4        5        6        7        9       10       12       13 
 8362871  7674136  7517068  6557111  8594098 10261070  7508457  8344505  7702105  7395758 

compare_result<- cbind(actual= test$price, predicted = price_pred)

number of rows of result is not a multiple of vector length (arg 1)

compare_result <- as.data.frame(compare_result)
error<- compare_result$actual- compare_result$predicted
cbind(compare_result,error)