June 2018 Update
This commit is contained in:
Ingy döt Net
parent
ba8067c3b7
commit
22f33d4004
5278 changed files with 84726 additions and 14379 deletions
|
|
@ -1,2 +1,2 @@
|
|||
---
|
||||
note: Matrices
|
||||
note: Probability and statistics
|
||||
|
|
|
|||
|
|
@ -12,20 +12,20 @@
|
|||
*
|
||||
* INPUT ARRAYS ARE DESTROYED!
|
||||
*
|
||||
*___Name_________Type_______________In/Out____Description________________________
|
||||
* X(N,K) Double precision In Predictors
|
||||
* Y(N) Double precision Both On input: N Observations
|
||||
* On output: K beta weights
|
||||
* N Integer In Number of observations
|
||||
* K Integer In Number of predictor variables
|
||||
* DWORK(3*K) Double precision Neither Workspace
|
||||
* IWORK(K) Integer Neither Workspace
|
||||
*___Name___________Type_______________In/Out____Description_____________
|
||||
* X(N,K) Double precision In Predictors
|
||||
* Y(N) Double precision Both On input: N Observations
|
||||
* On output: K beta weights
|
||||
* N Integer In Number of observations
|
||||
* K Integer In Number of predictor variables
|
||||
* DWORK(N+2*K) Double precision Neither Workspace
|
||||
* IWORK(K) Integer Neither Workspace
|
||||
*-----------------------------------------------------------------------
|
||||
SUBROUTINE MR (X, Y, N, K, DWORK, IWORK)
|
||||
IMPLICIT NONE
|
||||
INTEGER K, N, IWORK
|
||||
DOUBLE PRECISION X, Y, DWORK
|
||||
DIMENSION X(N,K), Y(N), DWORK(3*K), IWORK(K)
|
||||
DIMENSION X(N,K), Y(N), DWORK(N+2*K), IWORK(K)
|
||||
|
||||
* local variables
|
||||
INTEGER I, J
|
||||
|
|
@ -44,7 +44,7 @@
|
|||
|
||||
* call function
|
||||
CALL DHFTI (X, N, N, K, Y, N, 1, TAU,
|
||||
$ J, DWORK(1), DWORK(K+1), DWORK(2*K+1), IWORK)
|
||||
$ J, DWORK(1), DWORK(N+1), DWORK(N+K+1), IWORK)
|
||||
IF (J < K) PRINT *, 'mr: solution is rank deficient!'
|
||||
RETURN
|
||||
END ! of MR
|
||||
|
|
@ -55,7 +55,7 @@
|
|||
INTEGER N, K
|
||||
PARAMETER (N=15, K=3)
|
||||
INTEGER IWORK(K), I, J
|
||||
DOUBLE PRECISION XIN(N), X(N,K), Y(N), DWORK(3*K)
|
||||
DOUBLE PRECISION XIN(N), X(N,K), Y(N), DWORK(N+2*K)
|
||||
|
||||
DATA XIN / 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68,
|
||||
$ 1.70, 1.73, 1.75, 1.78, 1.80, 1.83 /
|
||||
|
|
|
|||
121
Task/Multiple-regression/Kotlin/multiple-regression.kotlin
Normal file
121
Task/Multiple-regression/Kotlin/multiple-regression.kotlin
Normal file
|
|
@ -0,0 +1,121 @@
|
|||
// Version 1.2.31
|
||||
|
||||
typealias Vector = DoubleArray
|
||||
typealias Matrix = Array<Vector>
|
||||
|
||||
operator fun Matrix.times(other: Matrix): Matrix {
|
||||
val rows1 = this.size
|
||||
val cols1 = this[0].size
|
||||
val rows2 = other.size
|
||||
val cols2 = other[0].size
|
||||
require(cols1 == rows2)
|
||||
val result = Matrix(rows1) { Vector(cols2) }
|
||||
for (i in 0 until rows1) {
|
||||
for (j in 0 until cols2) {
|
||||
for (k in 0 until rows2) {
|
||||
result[i][j] += this[i][k] * other[k][j]
|
||||
}
|
||||
}
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
fun Matrix.transpose(): Matrix {
|
||||
val rows = this.size
|
||||
val cols = this[0].size
|
||||
val trans = Matrix(cols) { Vector(rows) }
|
||||
for (i in 0 until cols) {
|
||||
for (j in 0 until rows) trans[i][j] = this[j][i]
|
||||
}
|
||||
return trans
|
||||
}
|
||||
|
||||
fun Matrix.inverse(): Matrix {
|
||||
val len = this.size
|
||||
require(this.all { it.size == len }) { "Not a square matrix" }
|
||||
val aug = Array(len) { DoubleArray(2 * len) }
|
||||
for (i in 0 until len) {
|
||||
for (j in 0 until len) aug[i][j] = this[i][j]
|
||||
// augment by identity matrix to right
|
||||
aug[i][i + len] = 1.0
|
||||
}
|
||||
aug.toReducedRowEchelonForm()
|
||||
val inv = Array(len) { DoubleArray(len) }
|
||||
// remove identity matrix to left
|
||||
for (i in 0 until len) {
|
||||
for (j in len until 2 * len) inv[i][j - len] = aug[i][j]
|
||||
}
|
||||
return inv
|
||||
}
|
||||
|
||||
fun Matrix.toReducedRowEchelonForm() {
|
||||
var lead = 0
|
||||
val rowCount = this.size
|
||||
val colCount = this[0].size
|
||||
for (r in 0 until rowCount) {
|
||||
if (colCount <= lead) return
|
||||
var i = r
|
||||
|
||||
while (this[i][lead] == 0.0) {
|
||||
i++
|
||||
if (rowCount == i) {
|
||||
i = r
|
||||
lead++
|
||||
if (colCount == lead) return
|
||||
}
|
||||
}
|
||||
|
||||
val temp = this[i]
|
||||
this[i] = this[r]
|
||||
this[r] = temp
|
||||
|
||||
if (this[r][lead] != 0.0) {
|
||||
val div = this[r][lead]
|
||||
for (j in 0 until colCount) this[r][j] /= div
|
||||
}
|
||||
|
||||
for (k in 0 until rowCount) {
|
||||
if (k != r) {
|
||||
val mult = this[k][lead]
|
||||
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
|
||||
}
|
||||
}
|
||||
|
||||
lead++
|
||||
}
|
||||
}
|
||||
|
||||
fun printVector(v: Vector) {
|
||||
println(v.asList())
|
||||
println()
|
||||
}
|
||||
|
||||
fun multipleRegression(y: Vector, x: Matrix): Vector {
|
||||
val cy = (arrayOf(y)).transpose() // convert 'y' to column vector
|
||||
val cx = x.transpose() // convert 'x' to column vector array
|
||||
return ((x * cx).inverse() * x * cy).transpose()[0]
|
||||
}
|
||||
|
||||
fun main(args: Array<String>) {
|
||||
var y = doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0)
|
||||
var x = arrayOf(doubleArrayOf(2.0, 1.0, 3.0, 4.0, 5.0))
|
||||
var v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
|
||||
y = doubleArrayOf(3.0, 4.0, 5.0)
|
||||
x = arrayOf(
|
||||
doubleArrayOf(1.0, 2.0, 1.0),
|
||||
doubleArrayOf(1.0, 1.0, 2.0)
|
||||
)
|
||||
v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
|
||||
y = doubleArrayOf(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
|
||||
63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46)
|
||||
|
||||
val a = doubleArrayOf(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70,
|
||||
1.73, 1.75, 1.78, 1.80, 1.83)
|
||||
x = arrayOf(DoubleArray(a.size) { 1.0 }, a, a.map { it * it }.toDoubleArray())
|
||||
v = multipleRegression(y, x)
|
||||
printVector(v)
|
||||
}
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
clear
|
||||
set seed 17760704
|
||||
set obs 200
|
||||
forv i=1/4 {
|
||||
gen x`i'=rnormal()
|
||||
}
|
||||
gen y=1.5+0.8*x1-0.7*x2+1.1*x3-1.7*x4+rnormal()
|
||||
|
|
@ -0,0 +1 @@
|
|||
reg y x*
|
||||
11
Task/Multiple-regression/Stata/multiple-regression-3.stata
Normal file
11
Task/Multiple-regression/Stata/multiple-regression-3.stata
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
. di _b[x1]
|
||||
.75252466
|
||||
|
||||
. di _b[_cons]
|
||||
1.3991314
|
||||
|
||||
. di _se[x1]
|
||||
.06895593
|
||||
|
||||
. di _se[_cons]
|
||||
.06978623
|
||||
25
Task/Multiple-regression/Stata/multiple-regression-4.stata
Normal file
25
Task/Multiple-regression/Stata/multiple-regression-4.stata
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
. estat ic
|
||||
|
||||
Akaike's information criterion and Bayesian information criterion
|
||||
|
||||
-----------------------------------------------------------------------------
|
||||
Model | Obs ll(null) ll(model) df AIC BIC
|
||||
-------------+---------------------------------------------------------------
|
||||
. | 200 -487.1455 -275.6985 5 561.397 577.8886
|
||||
-----------------------------------------------------------------------------
|
||||
Note: N=Obs used in calculating BIC; see [R] BIC note.
|
||||
|
||||
. estat vce
|
||||
|
||||
Covariance matrix of coefficients of regress model
|
||||
|
||||
e(V) | x1 x2 x3 x4 _cons
|
||||
-------------+------------------------------------------------------------
|
||||
x1 | .00475492
|
||||
x2 | -.00040258 .00486445
|
||||
x3 | -.00042516 .00017355 .00521125
|
||||
x4 | -.00011915 -.0002568 .00054646 .00386583
|
||||
_cons | .00030777 -.00031109 -.00023794 .00058926 .00487012
|
||||
|
||||
. predict yhat, xb
|
||||
. predict r, r
|
||||
Loading…
Add table
Add a link
Reference in a new issue