#Loading data
housing_data <- read.csv("C:\\Users\\Toshiba\\Downloads\\archive (4)\\Housing.csv", header = TRUE, sep = ",")summary(housing_data)## price area bedrooms bathrooms
## Min. : 1750000 Min. : 1650 Min. :1.000 Min. :1.000
## 1st Qu.: 3430000 1st Qu.: 3600 1st Qu.:2.000 1st Qu.:1.000
## Median : 4340000 Median : 4600 Median :3.000 Median :1.000
## Mean : 4766729 Mean : 5151 Mean :2.965 Mean :1.286
## 3rd Qu.: 5740000 3rd Qu.: 6360 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :13300000 Max. :16200 Max. :6.000 Max. :4.000
## stories mainroad guestroom basement
## Min. :1.000 Length:545 Length:545 Length:545
## 1st Qu.:1.000 Class :character Class :character Class :character
## Median :2.000 Mode :character Mode :character Mode :character
## Mean :1.806
## 3rd Qu.:2.000
## Max. :4.000
## hotwaterheating airconditioning parking prefarea
## Length:545 Length:545 Min. :0.0000 Length:545
## Class :character Class :character 1st Qu.:0.0000 Class :character
## Mode :character Mode :character Median :0.0000 Mode :character
## Mean :0.6936
## 3rd Qu.:1.0000
## Max. :3.0000
## furnishingstatus
## Length:545
## Class :character
## Mode :character
##
##
## summary(housing_data)## price area bedrooms bathrooms
## Min. : 1750000 Min. : 1650 Min. :1.000 Min. :1.000
## 1st Qu.: 3430000 1st Qu.: 3600 1st Qu.:2.000 1st Qu.:1.000
## Median : 4340000 Median : 4600 Median :3.000 Median :1.000
## Mean : 4766729 Mean : 5151 Mean :2.965 Mean :1.286
## 3rd Qu.: 5740000 3rd Qu.: 6360 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :13300000 Max. :16200 Max. :6.000 Max. :4.000
## stories mainroad guestroom basement
## Min. :1.000 Length:545 Length:545 Length:545
## 1st Qu.:1.000 Class :character Class :character Class :character
## Median :2.000 Mode :character Mode :character Mode :character
## Mean :1.806
## 3rd Qu.:2.000
## Max. :4.000
## hotwaterheating airconditioning parking prefarea
## Length:545 Length:545 Min. :0.0000 Length:545
## Class :character Class :character 1st Qu.:0.0000 Class :character
## Mode :character Mode :character Median :0.0000 Mode :character
## Mean :0.6936
## 3rd Qu.:1.0000
## Max. :3.0000
## furnishingstatus
## Length:545
## Class :character
## Mode :character
##
##
## variance_values <- sapply(housing_data[, sapply(housing_data, is.numeric)], var)
print("Variance Values:")## [1] "Variance Values:"print(variance_values)## price area bedrooms bathrooms stories parking
## 3.498544e+12 4.709512e+06 5.447383e-01 2.524757e-01 7.525432e-01 7.423300e-01covariance_matrix <- cov(housing_data[, sapply(housing_data, is.numeric)])
print("Covariance Matrix:")## [1] "Covariance Matrix:"print(covariance_matrix)## price area bedrooms bathrooms stories
## price 3.498544e+12 2.175676e+09 5.059464e+05 4.864093e+05 6.826446e+05
## area 2.175676e+09 4.709512e+06 2.432321e+02 2.113466e+02 1.581294e+02
## bedrooms 5.059464e+05 2.432321e+02 5.447383e-01 1.386738e-01 2.615893e-01
## bathrooms 4.864093e+05 2.113466e+02 1.386738e-01 2.524757e-01 1.421715e-01
## stories 6.826446e+05 1.581294e+02 2.615893e-01 1.421715e-01 7.525432e-01
## parking 6.194673e+05 6.599897e+02 8.856247e-02 7.684161e-02 3.404277e-02
## parking
## price 6.194673e+05
## area 6.599897e+02
## bedrooms 8.856247e-02
## bathrooms 7.684161e-02
## stories 3.404277e-02
## parking 7.423300e-01correlation_matrix <- cor(housing_data[, sapply(housing_data, is.numeric)])
print("Correlation Matrix:")## [1] "Correlation Matrix:"print(correlation_matrix)## price area bedrooms bathrooms stories parking
## price 1.0000000 0.53599735 0.3664940 0.5175453 0.42071237 0.38439365
## area 0.5359973 1.00000000 0.1518585 0.1938195 0.08399605 0.35298048
## bedrooms 0.3664940 0.15185849 1.0000000 0.3739302 0.40856424 0.13926990
## bathrooms 0.5175453 0.19381953 0.3739302 1.0000000 0.32616471 0.17749582
## stories 0.4207124 0.08399605 0.4085642 0.3261647 1.00000000 0.04554709
## parking 0.3843936 0.35298048 0.1392699 0.1774958 0.04554709 1.00000000eigen_results <- eigen(correlation_matrix)print("Eigen Values:")## [1] "Eigen Values:"print(eigen_results$values)## [1] 2.5561051 1.2171486 0.6771415 0.6566698 0.5908395 0.3020955print("Eigen Vectors:")## [1] "Eigen Vectors:"print(eigen_results$vectors)## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.5395439 0.1203486 0.24279104 0.04162299 -0.14135501 0.78342034
## [2,] -0.3685384 0.5178529 0.51575760 -0.22455991 0.31542421 -0.42436114
## [3,] -0.3915181 -0.3822393 -0.38949056 -0.24634216 0.69703170 0.04864311
## [4,] -0.4322131 -0.2116685 0.01788812 0.81460710 -0.03855905 -0.32093105
## [5,] -0.3682862 -0.4917297 0.12475034 -0.46684594 -0.55146176 -0.29146070
## [6,] -0.3119977 0.5335130 -0.71236303 -0.07500705 -0.29845646 -0.12592842