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HP Prime for advance statistics - pr011235 - 09-04-2014 07:02 AM
Does anyone know of a one way anova and or multiple regression app that can be loaded to the HP Prime?
RE: HP Prime for advance statistics - Namir - 09-04-2014 03:28 PM
(09-04-2014 07:02 AM)pr011235 Wrote: Does anyone know of a one way anova and or multiple regression app that can be loaded to the HP Prime?
I am attaching a pdf file that contains several articles (from the HP Solve newsletter) for the HP 39gII that perform ADVANCED types of regression. These programs should work with the HP Prime. These programs show the power of the HP 39gII and the HP Prime in performing sophisticated regression calculations.
Namir
PS: Here is the code for about the dozen programs in the attached article, so you can copy and pasted them easily in the HP Prime emulator or the Connectivity Kit.
MLR2
Code:
EXPORT MLR2(MatX,VectY)
BEGIN
LOCAL i,j,y,Rsqr;
LOCAL lstDimX,NumRowsX;
LOCAL YMean,Sum1,Sum2,Yhat,RegCoeff;
// calculate the regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate the number of data points
lstDimX:=SIZE(MatX);
NumRowsX:=lstDimX(1);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRowsX DO
y:=VectY(i,1);
Sum1:=Sum1+y;
END;
YMean:=Sum1/NumRowsX;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
// return the results
RETURN {Rsqr,RegCoeff};
END;PolyReg
Code:
EXPORT PolyReg(DSMat,SelXCol,SelYCol,Order)
BEGIN
LOCAL i,j,x,y;
LOCAL lstDimX,NumRows;
LOCAL MatX, VectY, RegCoeff;
LOCAL YMean,Sum1,Sum2,Yhat,Rsqr;
lstDimX:=SIZE(DSMat);
NumRows:=lstDimX(1);
// initialize matrix and vector
MatX:=MAKEMAT(1,NumRows,Order+1);
VectY:=MAKEMAT(1,NumRows,1);
Sum1:=0;
// populate matrix X and vector y with data
FOR i FROM 1 TO NumRows DO
y:=DSMat(i,SelYCol);
x:=DSMat(i,SelXCol);
VectY(i,1):=y;
Sum1:=Sum1+y;
FOR j FROM 1 TO Order DO
MatX(i,j+1):=x^j;
END;
END;
// calculate ymean
YMean:=Sum1/NumRows;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate the sums of squares of
// (yhat - ymean) and (y - ymean)
Sum1:=0;
Sum2:=0;
FOR i FROM 1 TO NumRows DO
y:=DSMat(i,SelYCol);
x:=DSMat(i,SelXCol);
Yhat:=RegCoeff(1,1);
FOR j FROM 1 TO Order DO
Yhat:=Yhat+RegCoeff(j+1,1)*x^j;
END;
Sum1:=Sum1+(Yhat-YMean)^2;
Sum2:=Sum2+(y-YMean)^2;
END;
// calculate coefficient of determination
Rsqr:=Sum1/Sum2;
RETURN {Rsqr,RegCoeff};
END;PowerFit
Code:
EXPORT PowerFit(MatX,VectY)
BEGIN
LOCAL i,j;
LOCAL lstDimX,NumRowsX,NumColsX;
LOCAL TMatX,TVectY,RegCoeff,Rsqr;
LOCAL YMean,Sum1,Sum2,Yhat;
// get the number of rows and columns of matrix MatX
lstDimX:=SIZE(MatX);
NumRowsX:=lstDimX(1);
NumColsX:=lstDimX(2);
// create matrices to store transformed data
TMatX:=MAKEMAT(1,NumRowsX,NumColsX+1);
TVectY:=MAKEMAT(1,NumRowsX,1);
FOR i FROM 1 TO NumRowsX DO
TVectY(i,1):=LN(VectY(i,1));
FOR j FROM 1 TO NumColsX DO
TMatX(i,j+1):=LN(MatX(i,j));
END;
END;
// calculate the regression coefficients
RegCoeff:=LSQ(TMatX,TVectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+TVectY(i,1);
END;
YMean:=Sum1/NumRowsX;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=TMatX*RegCoeff;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(TVectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
// return the results
RETURN {Rsqr,RegCoeff};
END;LinearizedReg
Code:
EXPORT LinearizedReg(DSMat,lstSelXData,lstSelYData)
BEGIN
LOCAL i,x,y;
LOCAL lstDimX,NumRowsX;
LOCAL MatX,VectY,RegCoeff;
LOCAL SelXCol,ShiftX,ScaleX,PowerX;
LOCAL SelYCol,ShiftY,ScaleY,PowerY;
LOCAL Sum1,Sum2,YMean,Yhat,Rsqr;
lstDimX:=SIZE(DSMat);
NumRowsX:=lstDimX(1);
// get parameters for x
SelXCol:=lstSelXData(1);
ShiftX:=lstSelXData(2);
ScaleX:=lstSelXData(3);
PowerX:=lstSelXData(4);
// get parameters for y
SelYCol:=lstSelYData(1);
ShiftY:=lstSelYData(2);
ScaleY:=lstSelYData(3);
PowerY:=lstSelYData(4);
// create regression matrix and vector
MatX:=MAKEMAT(1,NumRowsX,2);
VectY:=MAKEMAT(1,NumRowsX,1);
// populate matrix and vector
FOR i FROM 1 TO NumRowsX DO
x:=ScaleX*DSMat(i,SelXCol)+ShiftX;
y:=ScaleY*DSMat(i,SelYCol)+ShiftY;
// transform x
IF PowerX==0 THEN
x:=LN(x);
ELSE
x:=x^PowerX;
END;
// transform y
IF PowerY==0 THEN
y:=LN(y);
ELSE
y:=y^PowerY;
END;
MatX(i,2):=x;
VectY(i,1):=y;
END;
// calculate coefficient of determination
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRowsX DO
y:=VectY(i,1);
Sum1:=Sum1+y;
END;
YMean:=Sum1/NumRowsX;
// calculate coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
RETURN {Rsqr,RegCoeff};
END;LinearizedReg3
Code:
EXPORT LinearizedReg3(DSMat,lstSelXData,lstSelZData,lstSelYData)
BEGIN
LOCAL i,x,y,z;
LOCAL lstDimX,NumRowsX;
LOCAL MatX,VectY,RegCoeff;
LOCAL SelXCol,ShiftX,ScaleX,PowerX;
LOCAL SelYCol,ShiftY,ScaleY,PowerY;
LOCAL SelZCol,ShiftZ,ScaleZ,PowerZ;
LOCAL Sum1,Sum2,YMean,Yhat,Rsqr;
lstDimX:=SIZE(DSMat);
NumRowsX:=lstDimX(1);
SelXCol:=lstSelXData(1);
ShiftX:=lstSelXData(2);
ScaleX:=lstSelXData(3);
PowerX:=lstSelXData(4);
// get parameters for z
SelZCol:=lstSelZData(1);
ShiftZ:=lstSelZData(2);
ScaleZ:=lstSelZData(3);
PowerZ:=lstSelZData(4);
// get parameters for y
SelYCol:=lstSelYData(1);
ShiftY:=lstSelYData(2);
ScaleY:=lstSelYData(3);
PowerY:=lstSelYData(4);
// create regression matrix and vector
MatX:=MAKEMAT(1,NumRowsX,3);
VectY:=MAKEMAT(1,NumRowsX,1);
// populate matrix and vector
FOR i FROM 1 TO NumRowsX DO
x:=ScaleX*DSMat(i,SelXCol)+ShiftX;
y:=ScaleY*DSMat(i,SelYCol)+ShiftY;
z:=ScaleZ*DSMat(i,SelZCol)+ShiftZ;
// transform x
IF PowerX==0 THEN
x:=LN(x);
ELSE
x:=x^PowerX;
END;
// transform z
IF PowerZ==0 THEN
z:=LN(z);
ELSE
z:=z^PowerZ;
END;
// transform y
IF PowerY==0 THEN
y:=LN(y);
ELSE
y:=y^PowerY;
END;
MatX(i,2):=x;
MatX(i,3):=z;
VectY(i,1):=y;
END;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRowsX DO
y:=VectY(i,1);
Sum1:=Sum1+y;
END;
YMean:=Sum1/NumRowsX;
// calculate coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
RETURN {Rsqr,RegCoeff};
END;MLRX
Code:
EXPORT MLRX(DSMat,MaxTerms,TrnfMat)
BEGIN
LOCAL i,j,x,Rsqr;
LOCAL lstDimX,lstDimT,NumRowsX,NumColsX;
LOCAL MatX,VectY,RegCoeff;
LOCAL SelXCol,Shift,Scale,PowerX;
LOCAL InsMat,InsCol,NumTrnf;
LOCAL YMean,Sum1,Sum2,Yhat;
// calculate the number of data points
lstDimX:=SIZE(DSMat);
NumRowsX:=lstDimX(1);
NumColsX:=lstDimX(2);
// get the number of transformations
lstDimT:=SIZE(TrnfMat);
NumTrnf:=lstDimT(1);
// create the data matrices
MatX:=MAKEMAT(1,NumRowsX,MaxTerms+1);
VectY:=MAKEMAT(1,NumRowsX,1);
FOR j FROM 1 TO NumTrnf DO
// get the transformation/insertion parameters
SelXCol:=TrnfMat[j,1];
Scale:=TrnfMat[j,2];
Shift:=TrnfMat[j,3];
PowerX:=TrnfMat[j,4];
InsMat:=TrnfMat[j,5];
InsCol:=TrnfMat[j,6];
// process all rows for current variable selection,
// transformation, and insertion
FOR i FROM 1 TO NumRowsX DO
// get x
x:=DSMat[i,SelXCol];
// transform x by scaling and shifting
x:=Scale*x+Shift;
// raise x to power or take ln() value
IF PowerX==0 THEN
x:=LN(x);
ELSE
x:=x^PowerX;
END;
// insert in targeted matrix
IF InsMat>0 THEN
// insert in matrix of independent variables
IF InsCol>(MaxTerms+1) THEN
// display an error message
MSGBOX("Column "+InsCol+" is outside the range of columns");
RETURN "ERROR";
END;
MatX[i,InsCol]:=MatX[i,InsCol]*x;
ELSE
// insert in vector of dependent variable
VectY[i,1]:=VectY[i,1]*x;
END;
END;
END;
// calculate the regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+VectY(i,1);
END;
YMean:=Sum1/NumRowsX;
// calculate the correlation coefficient
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRowsX DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
// return the results
RETURN {Rsqr,RegCoeff};
END;BestLR
Code:
EXPORT BestLR(Data,lstSel,lstX,lstY)
BEGIN
LOCAL Tx,Ty,i,j,k;
LOCAL SelXCol,SelYCol;
LOCAL PowerX,PowerY;
LOCAL MatX,VectY,RegCoeff,MatRes;
LOCAL lstDim,NumRows,ResUpdated;
LOCAL Sum1,Sum2,Rsqr,YMean,Yhat;
LOCAL MaxRes,NumColRes;
// use the default transformation list
// for variable x if lstX is empty
IF SIZE(lstX)==0 THEN
lstX:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use the default transformation list
// for variable y if lstY is empty
IF SIZE(lstY)==0 THEN
lstY:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// set the maximum number of results
MaxRes:=20;
// set the number of columns in
// the results matrix
NumColRes:=5;
// get the indices for variable x and y
SelXCol:=lstSel(1);
SelYCol:=lstSel(2);
// get the number of rows of data
lstDim:=SIZE(Data);
NumRows:=lstDim(1);
// create the result and regression matrices
MatX:=MAKEMAT(1,NumRows,2);
VectY:=MAKEMAT(1,NumRows,1);
MatRes:= MAKEMAT(0,MaxRes,NumColRes);
// iterate for each transformation in x
FOR Tx FROM 1 TO SIZE(lstX) DO
// get the current power of x
PowerX:=lstX(Tx);
// transform x
IF PowerX==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,2):=LN(Data(i,SelXCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,2):=Data(i,SelXCol)^PowerX;
END;
END;
// iterate for each transformation in y
FOR Ty FROM 1 TO SIZE(lstY) DO
// get the current power of y
PowerY:=lstY(Ty);
// transform y
IF PowerY==0 THEN
FOR i FROM 1 TO NumRows DO
VectY(i,1):=LN(Data(i,SelYCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
VectY(i,1):=Data(i,SelYCol)^PowerY;
END;
END;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:= 0;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+VectY(i,1);
END;
YMean:=Sum1/NumRows;
// calculate coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
// Rsqr is better than last entry
// in the results matrix?
IF Rsqr>MatRes(MaxRes,1) THEN
ResUpdated:=0;
// loop for each row in the
// results matrix
FOR i FROM 1 TO MaxRes DO
// compare with other Rsqr values
IF ResUpdated==0 AND Rsqr>MatRes(i,1) THEN
// found better Rsqr for row i
// push rows below?
IF i<MaxRes THEN
j:=MaxRes-1;
REPEAT
// FOR j FROM MaxRes-1 TO n STEP -1 DO
FOR k FROM 1 TO NumColRes DO
MatRes(j+1,k):=MatRes(j,k);
END;
j:=j-1;
//END;
UNTIL j<i;
END;
// store new best results
MatRes(i,1):=Rsqr;
MatRes(i,2):=PowerY;
MatRes(i,3):=PowerX;
MatRes(i,4):=RegCoeff(1,1);
MatRes(i,5):=RegCoeff(2,1);
ResUpdated:=1;
END;
END;
END;
END; // FOR Ty
END; // FOR Tx
RETURN MatRes;
END;BestMLR2
Code:
EXPORT BestMLR2(Data,lstSel,lstX,lstZ,lstY)
BEGIN
LOCAL Tx,Tz,Ty,i,j,k;
LOCAL SelXCol,SelZCol,SelYCol;
LOCAL PowerX,PowerZ,PowerY;
LOCAL MatX,VectY,RegCoeff,MatRes;
LOCAL lstDim,NumRows,ResUpdated;
LOCAL Sum1,Sum2,Rsqr,YMean,Yhat;
LOCAL MaxRes,NumColRes;
// use default transformation list
// if lstX is an empty list
IF SIZE(lstX)==0 THEN
lstX:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use default transformation list
// if lstZ is an empty list
IF SIZE(lstZ)==0 THEN
lstZ:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use default transformation list
// if lstY is an empty list
IF SIZE(lstY)==0 THEN
lstY:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// Set the number of rows and columns in the results matrix
MaxRes:=20;
NumColRes:=7;
// get the variable selectors
SelXCol:=lstSel(1);
SelZCol:=lstSel(2);
SelYCol:=lstSel(3);
// get the number of rows in matrix Data
lstDim:=SIZE(Data);
NumRows:=lstDim(1);
// create the regression and results matrices
MatX:=MAKEMAT(1,NumRows,3);
VectY:=MAKEMAT(1,NumRows,1);
MatRes:=MAKEMAT(0,MaxRes,NumColRes);
// start the calculations
// process transformations for variable x
FOR Tx FROM 1 TO SIZE(lstX) DO
PowerX:=lstX(Tx);
// transform x
IF PowerX==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,2):=LN(Data(i,SelXCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,2):=Data(i,SelXCol)^PowerX;
END;
END;
// process transformations for variable z
FOR Tz FROM 1 TO SIZE(lstZ) DO
PowerZ:=lstZ(Tz);
// transform z
IF PowerZ==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,3):=LN(Data(i,SelZCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,3):=Data(i,SelZCol)^PowerZ;
END;
END;
// process transformations for variable y
FOR Ty FROM 1 TO SIZE(lstY) DO
PowerY:=lstY(Ty);
// transform y
IF PowerY==0 THEN
FOR i FROM 1 TO NumRows DO
VectY(i,1):=LN(Data(i,SelYCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
VectY(i,1):=Data(i,SelYCol)^PowerY;
END;
END;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+VectY(i,1);
END;
Ymean:=Sum1/NumRows;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+(Yhat(i,1)-Ymean)^2;
Sum2:=Sum2+(VectY(i,1)-Ymean)^2;
END;
Rsqr:=Sum1/Sum2;
// Rsqr is better than last entry
// in the results matrix?
IF Rsqr>MatRes(MaxRes,1) THEN
ResUpdated:=0;
// check which row to insert better
// regression results
FOR i FROM 1 TO MaxRes DO
// insert new results in row i?
IF ResUpdated==0 AND Rsqr>MatRes(i,1) THEN
// inserting inside the results matrix?
IF i<MaxRes THEN
// downward copy rows from MaxRes-1 to i
j:=MaxRes-1;
REPEAT
FOR k FROM 1 TO NumColRes DO
MatRes(j+1,k):=MatRes(j,k);
END;
j:=j-1;
UNTIL j<i;
END;
// insert better results in row i
MatRes(i,1):=Rsqr;
MatRes(i,2):=PowerY;
MatRes(i,3):=PowerX;
MatRes(i,4):=PowerZ;
FOR k FROM 1 TO 3 DO
MatRes(i,4+k):=RegCoeff(k,1);
END;
ResUpdated:=1;
END;
END;
END;
END; // FOR Ty
END; // FOR Tz
END; // FOR Tx
RETURN MatRes;
END;BestPolyReg
Code:
EXPORT BestPolyReg(Data,SelXCol,SelYCol,MinOrder,MaxOrder)
BEGIN
LOCAL i,k,x,y,Order;
LOCAL MatX,VectY;
LOCAL lstDim,NumRows;
LOCAL Sum1,Sum2,Sum3,AICc,BestAICc;
LOCAL Rsqr,RsqrAdj,YMean,Yhat,RegCoeff;
LOCAL BestOrder,BestRsqr,BestRsqrAdj,BestRegCoeff;
lstDim:=SIZE(Data);
NumRows:=lstDim(1);
IF MinOrder<1 THEN
MinOrder:=1;
END;
// initialize best regression data
BestOrder=0;
BestRsqr:=0;
BestRsqrAdj=0;
BestAICc:=1E499;
// initialize vector y
VectY:=MAKEMAT(1,NumRows,1);
// calculate ymean … needs to be done once!
Sum1:=0;
FOR i FROM 1 TO NumRows DO
y:=Data(i,SelYCol);
VectY(i,1):=y;
Sum1:=Sum1+y;
END;
YMean:=Sum1/NumRows;
// calculate sum of y – ymean squared
Sum2:=0;
FOR i FROM 1 TO NumRows DO
y:=Data(i,SelYCol);
Sum2:=Sum2+(y-YMean)^2;
END;
// iterate for the specified range of polynomial orders
FOR Order FROM MinOrder TO MaxOrder DO
// (re)create the matrix MatX
MatX:=MAKEMAT(1,NumRows,1+Order);
// fill the columns to to Order+1 with x^power values
FOR i FROM 1 TO NumRows DO
x:=Data(i,SelXCol);
FOR k FROM 1 TO Order DO
MatX(i,k+1):=x^k;
END;
END;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate the coefficient of determination
Sum1:=0;
Sum3:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum3:=Sum3+(VectY(i,1)-Yhat(i,1))^2;
END;
Rsqr:=Sum1/Sum2;
// calculate the adjusted coefficient of determination
RsqrAdj:=1-(1-Rsqr)*(NumRows-1)/(NumRows-Order-1);
k:=Order+1;
// if Sum3 is 0 then adjust it to a small value
// to avoid getting a LN(0) error
IF Sum3==0 THEN
Sum3:=1E-499;
END;
// calculate AICc statistic
AICc:=NumRows*LN(Sum3/NumRows)+2*k+(2*k*(k+1))/(NumRows-k-1);
// display intermediate results
PRINT("Order="+Order+", AICc="+AICc+", Sum3="+Sum3);
// found a better fit?
IF AICc<BestAICc THEN
// update best regression data
BestOrder:=Order;
BestRsqr:=Rsqr;
BestRsqrAdj:=RsqrAdj;
BestAICc:=AICc;
BestRegCoeff:=RegCoeff;
END;
END;
RETURN {BestOrder,BestRsqr,BestRsqrAdj,BestAICc,BestRegCoeff};
END;BestMLR3
Code:
EXPORT BestMLR3(Data,lstSel,lstX,lstZ,lstT,lstY)
BEGIN
LOCAL Tx,Tz,Ty,Tt,i,j,k;
LOCAL SelXCol,SelZCol,SelTCol,SelYCol;
LOCAL PowerX,PowerZ,PowerT,PowerY;
LOCAL MatX,VectY,RegCoeff,MatRes;
LOCAL lstDim,NumRows,ResUpdated;
LOCAL Sum1,Sum2,Rsqr,YMean,Yhat;
LOCAL MaxRes,NumColRes;
// use default transformation list
// if lstX is an empty list
IF SIZE(lstX)==0 THEN
lstX:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use default transformation list
// if lstZ is an empty list
IF SIZE(lstZ)==0 THEN
lstZ:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use default transformation list
// if lstT is an empty list
IF SIZE(lstT)==0 THEN
lstT:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
// use default transformation list
// if lstY is an empty list
IF SIZE(lstY)==0 THEN
lstY:={-3,-2,-1,-0.5,0,0.5,1,2,3};
END;
MaxRes:=20;
NumColRes:=9;
// get the variable selectors
SelXCol:=lstSel(1);
SelZCol:=lstSel(2);
SelTCol:=lstSel(3);
SelYCol:=lstSel(4);
// get the number of rows in matrix Data
lstDim:=SIZE(Data);
NumRows:=lstDim(1);
// create the regression and results matrices
MatX:=MAKEMAT(1,NumRows,3);
VectY:=MAKEMAT(1,NumRows,1);
MatRes:=MAKEMAT(0,MaxRes,NumColRes);
// start the calculations
// process transformations for variable x
FOR Tx FROM 1 TO SIZE(lstX) DO
PowerX:=lstX(Tx);
// transform x
IF PowerX==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,2):=LN(Data(i,SelXCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,2):=Data(i,SelXCol)^PowerX;
END;
END;
// process transformations for variable z
FOR Tz FROM 1 TO SIZE(lstZ) DO
PowerZ:=lstZ(Tz);
// transform z
IF PowerZ==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,3):=LN(Data(i,SelZCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,3):=Data(i,SelZCol)^PowerZ;
END;
END;
// process transformations for variable t
FOR Tt FROM 1 TO SIZE(lstT) DO
PowerT:=lstT(Tt);
// transform t
IF PowerT==0 THEN
FOR i FROM 1 TO NumRows DO
MatX(i,4):=LN(Data(i,SelTCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
MatX(i,4):=Data(i,SelTCol)^PowerT;
END;
END;
// process transformations for variable y
FOR Ty FROM 1 TO SIZE(lstY) DO
PowerY:=lstY(Ty);
// transform y
IF PowerY==0 THEN
FOR i FROM 1 TO NumRows DO
VectY(i,1):=LN(Data(i,SelYCol));
END;
ELSE
FOR i FROM 1 TO NumRows DO
VectY(i,1):=Data(i,SelYCol)^PowerY;
END;
END;
// calculate regression coefficients
RegCoeff:=LSQ(MatX,VectY);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+VectY(i,1);
END;
YMean:=Sum1/NumRows;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+(Yhat(i,1)-YMean)^2;
Sum2:=Sum2+(VectY(i,1)-YMean)^2;
END;
Rsqr:=Sum1/Sum2;
// Rsqr is better than last entry
// in the results matrix?
IF Rsqr>MatRes(MaxRes,1) THEN
ResUpdated:=0;
// check which row to insert better
// regression results
FOR i FROM 1 TO MaxRes DO
// insert new results in row i?
IF ResUpdated==0 AND Rsqr>MatRes(i,1) THEN
// inserting inside the results matrix?
IF i<MaxRes THEN
// downward copy rows from MaxRes-1 to i
j:=MaxRes-1;
REPEAT
FOR k FROM 1 TO NumColRes DO
MatRes(j+1,k):=MatRes(j,k);
END;
j:=j-1;
UNTIL j<i;
END;
// insert better results in row i
MatRes(i,1):=Rsqr;
MatRes(i,2):=PowerY;
MatRes(i,3):=PowerX;
MatRes(i,4):=PowerZ;
MatRes(i,5):=PowerT;
FOR k FROM 1 TO 4 DO
MatRes(i,5+k):=RegCoeff(k,1);
END;
ResUpdated:=1;
END;
END;
END;
END; // FOR Ty
END; // FOR Tt
END; // FOR Tz
END; // FOR Tx
RETURN MatRes;
END;RErMLR2
Code:
EXPORT RErMLR2(MatX,VectY)
BEGIN
LOCAL i,j,y,Rsqr;
LOCAL lstDimX,NumRows,NumCols;
LOCAL YMean,Sum1,Sum2,Yhat;
LOCAL TMatX,VectOnes,RegCoeff;
// calculate the number of observations and variables
lstDimX:=SIZE(MatX);
NumRows:=lstDimX(1);
NumCols:=lstDimX(2);
// create transformation matrices
TMatX:=MAKEMAT(1,NumRows,NumCols+1);
VectOnes:=MAKEMAT(1,NumRows,1);
FOR i FROM 1 TO NumRows DO
y:=VectY(i,1);
TMatX(i,1):=1/y;
FOR j FROM 1 TO NumCols DO
TMatX(i,j+1):=MatX(i,j)/y;
END;
END;
// calculate the regression coefficients
RegCoeff:=LSQ(TMatX,VectOnes);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRows DO
y:=VectY(i,1);
Sum1:=Sum1+y;
END;
YMean:=Sum1/NumRows;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
FOR i FROM 1 TO NumRows DO
y:=VectY(i,1);
Yhat:=RegCoeff(1,1);
FOR j FROM 1 TO NumCols DO
Yhat:=Yhat+RegCoeff(j+1,1)*MatX(i,j);
END;
Sum1:=Sum1+((Yhat-YMean)/y)^2;
Sum2:=Sum2+((y-YMean)/y)^2;
END;
Rsqr:=Sum1/Sum2;
// return the results as a list
RETURN {Rsqr,RegCoeff};
END;RErPolyReg
Code:
EXPORT RErPolyReg(DSMat,SelXCol,SelYCol,Order)
BEGIN
LOCAL i,j,x,y;
LOCAL lstDimX,NumRows;
LOCAL MatX,VectOnes,RegCoeff;
LOCAL YMean,Sum1,Sum2,Yhat,Rsqr;
// get the number of rows
lstDimX:=SIZE(DSMat);
NumRows:=lstDimX(1);
// create the regression matrices
MatX:=MAKEMAT(1,NumRows,Order+1);
VectOnes:=MAKEMAT(1,NumRows,1);
// populate the regression matrices
FOR i FROM 1 TO NumRows DO
y:=DSMat(i,SelYCol);
x:=DSMat(i,SelXCol);
MatX(i,1):=1/y;
FOR j FROM 1 TO Order DO
MatX(i,j+1):=(x^j)/y;
END;
END;
// calculate the regression coefficients
RegCoeff:=LSQ(MatX,VectOnes);
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+DSMat(i,SelYCol);
END;
YMean:=Sum1/NumRows;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
FOR i FROM 1 TO NumRows DO
x:=DSMat(i,SelXCol);
y:=DSMat(i,SelYCol);
Yhat:=RegCoeff(1,1);
FOR j FROM 1 TO Order DO
Yhat:=Yhat+RegCoeff(j+1,1)*x^j;
END;
Sum1:=Sum1+((Yhat-YMean)/y)^2;
Sum2:=Sum2+((y-YMean)/y)^2;
END;
Rsqr:=Sum1/Sum2;
// return the list of results
RETURN {Rsqr,RegCoeff};
END;RErPowerFit
Code:
EXPORT RErPowerFit(MatX,VectY)
BEGIN
LOCAL i,j,y,LnY;
LOCAL lstDimX,NumRows,NumCols;
LOCAL TMatX,VectOnes,RegCoeff,Rsqr;
LOCAL YMean,Sum1,Sum2,Yhat;
lstDimX:=SIZE(MatX);
NumRows:=lstDimX(1);
NumCols:=lstDimX(2);
TMatX:=MAKEMAT(1,NumRows,NumCols+1);
VectOnes:=MAKEMAT(1,NumRows,1);
Sum1:=0;
FOR i FROM 1 TO NumRows DO
LnY:=LN(VectY(i,1));
Sum1:=Sum1+LnY;
TMatX(i,1):=1/LnY;
FOR j FROM 1 TO NumCols DO
TMatX(i,j+1):=LN(MatX(i,j))/LnY;
END;
END;
// calculate regression coefficients
RegCoeff:=LSQ(TMatX,VectOnes);
// calculate mean ln(y)
YMean:=Sum1/NumRows;
// calculate coefficient of determination
Sum1:=0;
Sum2:=0;
FOR i FROM 1 TO NumRows DO
Yhat:=RegCoeff(1,1);
FOR j FROM 1 TO NumCols DO
Yhat:=Yhat+RegCoeff(j+1,1)*LN(MatX(i,j));
END;
y:=LN(VectY(i,1));
Sum1:=Sum1+((Yhat-YMean)/y)^2;
Sum2:=Sum2+((y-YMean)/y)^2;
END;
Rsqr:=Sum1/Sum2;
RETURN {Rsqr,RegCoeff};
END;RE: HP Prime for advance statistics - Helge Gabert - 09-04-2014 03:57 PM
Good info, thanks for sharing!
A quick and dirty linear regression can always be set up with LSQ, but the programs are helpful as they also contain regression diagnostics.
Is there a repository for other HP 39gII programs?
RE: HP Prime for advance statistics - Namir - 09-04-2014 07:24 PM
(09-04-2014 03:57 PM)Helge Gabert Wrote: Is there a repository for other HP 39gII programs?
Not specifically for the HP 39gII. It would be in the general area. I will copy my reply to the general area.
RE: HP Prime for advance statistics - salvomic - 03-08-2015 04:21 PM
my first draft for ANOVA with Prime is here.
RE: HP Prime for advance statistics - salvomic - 03-24-2015 07:48 PM
(09-04-2014 03:28 PM)Namir Wrote: BestMLR2
Code:
EXPORT BestMLR2(Data,lstSel,lstX,lstZ,lstY)
BEGIN
...
LOCAL Sum1,Sum2,Rsqr,YMean,Yhat;
...
// calculate ymean
Sum1:=0;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+VectY(i,1);
END;
Ymean:=Sum1/NumRows;
// calculate the coefficient of determination
Sum1:=0;
Sum2:=0;
Yhat:=MatX*RegCoeff;
FOR i FROM 1 TO NumRows DO
Sum1:=Sum1+(Yhat(i,1)-Ymean)^2;
Sum2:=Sum2+(VectY(i,1)-Ymean)^2;
...
END;
hi Namir,
in BestMLR2 there is a little typo: YMean and Ymean; to correct it I simply change the namevar in Local definition...
However is a very useful program!
All the suite of these programs should be inside the FW of Prime, perhaps with other programs to analyze multiple regression, thank you to have done them!
Salvo