data <- read.csv("Housing.csv", header = TRUE)
numeric_data <- data[, c("price", "area", "bedrooms", "bathrooms", "stories", "parking")]
cov_matrix <- cov(numeric_data)
print(cov_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-01
eigen_cov <- eigen(cov_matrix)
print(eigen_cov)$values
## eigen() decomposition
## $values
## [1] 3.498546e+12 3.356500e+06 7.345801e-01 5.958731e-01 3.626262e-01
## [6] 1.677009e-01
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9.999998e-01 6.218809e-04 2.350022e-07 2.360030e-07 -1.896406e-08
## [2,] 6.218809e-04 -9.999998e-01 -1.068146e-04 4.693651e-05 1.227917e-05
## [3,] 1.446162e-07 2.127405e-05 -4.831235e-01 -3.524835e-01 -7.742078e-01
## [4,] 1.390319e-07 2.715391e-05 -1.156247e-01 -7.418855e-02 -1.559105e-01
## [5,] 1.951224e-07 7.936672e-05 -7.760615e-01 -2.230034e-01 5.897316e-01
## [6,] 1.770643e-07 -8.185750e-05 3.885243e-01 -9.058261e-01 1.688515e-01
## [,6]
## [1,] 1.167426e-07
## [2,] -2.065080e-05
## [3,] 2.072422e-01
## [4,] -9.781712e-01
## [5,] 1.465063e-02
## [6,] -4.137110e-03
## [1] 3.498546e+12 3.356500e+06 7.345801e-01 5.958731e-01 3.626262e-01
## [6] 1.677009e-01
print(eigen_cov)$vectors
## eigen() decomposition
## $values
## [1] 3.498546e+12 3.356500e+06 7.345801e-01 5.958731e-01 3.626262e-01
## [6] 1.677009e-01
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9.999998e-01 6.218809e-04 2.350022e-07 2.360030e-07 -1.896406e-08
## [2,] 6.218809e-04 -9.999998e-01 -1.068146e-04 4.693651e-05 1.227917e-05
## [3,] 1.446162e-07 2.127405e-05 -4.831235e-01 -3.524835e-01 -7.742078e-01
## [4,] 1.390319e-07 2.715391e-05 -1.156247e-01 -7.418855e-02 -1.559105e-01
## [5,] 1.951224e-07 7.936672e-05 -7.760615e-01 -2.230034e-01 5.897316e-01
## [6,] 1.770643e-07 -8.185750e-05 3.885243e-01 -9.058261e-01 1.688515e-01
## [,6]
## [1,] 1.167426e-07
## [2,] -2.065080e-05
## [3,] 2.072422e-01
## [4,] -9.781712e-01
## [5,] 1.465063e-02
## [6,] -4.137110e-03
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9.999998e-01 6.218809e-04 2.350022e-07 2.360030e-07 -1.896406e-08
## [2,] 6.218809e-04 -9.999998e-01 -1.068146e-04 4.693651e-05 1.227917e-05
## [3,] 1.446162e-07 2.127405e-05 -4.831235e-01 -3.524835e-01 -7.742078e-01
## [4,] 1.390319e-07 2.715391e-05 -1.156247e-01 -7.418855e-02 -1.559105e-01
## [5,] 1.951224e-07 7.936672e-05 -7.760615e-01 -2.230034e-01 5.897316e-01
## [6,] 1.770643e-07 -8.185750e-05 3.885243e-01 -9.058261e-01 1.688515e-01
## [,6]
## [1,] 1.167426e-07
## [2,] -2.065080e-05
## [3,] 2.072422e-01
## [4,] -9.781712e-01
## [5,] 1.465063e-02
## [6,] -4.137110e-03
cor_matrix <- cor(numeric_data)
print(cor_matrix)
## price area bedrooms bathrooms stories parking
## price 1.0000000 0.53599735 0.3664940 0.5175453 0.42071237 0.38439365
## area 0.5359973 1.00000000 0.1518585 0.1938195 0.08399605 0.35298048
## bedrooms 0.3664940 0.15185849 1.0000000 0.3739302 0.40856424 0.13926990
## bathrooms 0.5175453 0.19381953 0.3739302 1.0000000 0.32616471 0.17749582
## stories 0.4207124 0.08399605 0.4085642 0.3261647 1.00000000 0.04554709
## parking 0.3843936 0.35298048 0.1392699 0.1774958 0.04554709 1.00000000
eigen_cor <- eigen(cor_matrix)
print(eigen_cor)$values
## eigen() decomposition
## $values
## [1] 2.5561051 1.2171486 0.6771415 0.6566698 0.5908395 0.3020955
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.5395439 0.1203486 0.24279104 0.04162299 -0.14135501 0.78342034
## [2,] -0.3685384 0.5178529 0.51575760 -0.22455991 0.31542421 -0.42436114
## [3,] -0.3915181 -0.3822393 -0.38949056 -0.24634216 0.69703170 0.04864311
## [4,] -0.4322131 -0.2116685 0.01788812 0.81460710 -0.03855905 -0.32093105
## [5,] -0.3682862 -0.4917297 0.12475034 -0.46684594 -0.55146176 -0.29146070
## [6,] -0.3119977 0.5335130 -0.71236303 -0.07500705 -0.29845646 -0.12592842
## [1] 2.5561051 1.2171486 0.6771415 0.6566698 0.5908395 0.3020955
print(eigen_cor)$vectors
## eigen() decomposition
## $values
## [1] 2.5561051 1.2171486 0.6771415 0.6566698 0.5908395 0.3020955
##
## $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
## [,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