M

mat►list()	Catalog >
mat►list(Matrix) ⇒ list Returns a list filled with the elements in Matrix. The elements are copied from Matrix row by row. Note: You can insert this function from the computer keyboard by typing mat@>list(...).

mat►list()

Catalog >

mat►list(Matrix) ⇒ list

Returns a list filled with the elements in Matrix. The elements are copied from Matrix row by row.

Note: You can insert this function from the computer keyboard by typing mat@>list(...).

max()	Catalog >
max(Value1, Value2) ⇒ expression max(List1, List2) ⇒ list max(Matrix1, Matrix2) ⇒ matrix Returns the maximum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the maximum value of each pair of corresponding elements.
max(List) ⇒ expression Returns the maximum element in list.
max(Matrix1) ⇒ matrix Returns a row vector containing the maximum element of each column in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see here. Note: See also min().

mean()	Catalog >
mean(List[, freqList]) ⇒ expression Returns the mean of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List.
mean(Matrix1[, freqMatrix]) ⇒ matrix Returns a row vector of the means of all the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see here.	In Rectangular vector format:

mean()

Catalog >

mean(List[, freqList]) ⇒ expression

Returns the mean of the elements in List.

Each freqList element counts the number of consecutive occurrences of the corresponding element in List.

mean(Matrix1[, freqMatrix]) ⇒ matrix

Returns a row vector of the means of all the columns in Matrix1.

Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1.

Empty (void) elements are ignored. For more information on empty elements, see here.

In Rectangular vector format:

median()

Catalog >

median(List[, freqList]) ⇒ expression

Returns the median of the elements in List.

Each freqList element counts the number of consecutive occurrences of the corresponding element in List.

median(Matrix1[, freqMatrix]) ⇒ matrix

Returns a row vector containing the medians of the columns in Matrix1.

Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1.

Notes:

•

All entries in the list or matrix must simplify to numbers.

•

Empty (void) elements in the list or matrix are ignored. For more information on empty elements, see here.

MedMed	Catalog >
MedMed X,Y [, Freq] [, Category, Include]] Computes the median-median line y = (m•x+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See here.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

MedMed

Catalog >

MedMed X,Y [, Freq] [, Category, Include]]

Computes the median-median line y = (m•x+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See here.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0.

Category is a list of numeric or string category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.RegEqn	Median-median line equation: m•x+b
stat.m, stat.b	Model coefficients
stat.Resid	Residuals from the median-median line
stat.XReg	List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories
stat.YReg	List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories
stat.FreqReg	List of frequencies corresponding to stat.XReg and stat.YReg

mid()	Catalog >
mid(sourceString, Start[, Count]) ⇒ string Returns Count characters from character string sourceString, beginning with character number Start. If Count is omitted or is greater than the dimension of sourceString, returns all characters from sourceString, beginning with character number Start. Count must be ≥ 0. If Count = 0, returns an empty string.
mid(sourceList, Start [, Count]) ⇒ list Returns Count elements from sourceList, beginning with element number Start. If Count is omitted or is greater than the dimension of sourceList, returns all elements from sourceList, beginning with element number Start. Count must be ≥ 0. If Count = 0, returns an empty list.
mid(sourceStringList, Start[, Count]) ⇒ list Returns Count strings from the list of strings sourceStringList, beginning with element number Start.

min()	Catalog >
min(Value1, Value2) ⇒ expression min(List1, List2) ⇒ list min(Matrix1, Matrix2) ⇒ matrix Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements.
min(List) ⇒ expression Returns the minimum element of List.
min(Matrix1) ⇒ matrix Returns a row vector containing the minimum element of each column in Matrix1. Note: See also max().

mirr()	Catalog >
mirr(financeRate,reinvestRate,CF0,CFList[,CFFreq]) Financial function that returns the modified internal rate of return of an investment. financeRate is the interest rate that you pay on the cash flow amounts. reinvestRate is the interest rate at which the cash flows are reinvested. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. Note: See also irr(), here.

mirr()

Catalog >

mirr(financeRate,reinvestRate,CF0,CFList[,CFFreq])

Financial function that returns the modified internal rate of return of an investment.

financeRate is the interest rate that you pay on the cash flow amounts.

reinvestRate is the interest rate at which the cash flows are reinvested.

CF0 is the initial cash flow at time 0; it must be a real number.

CFList is a list of cash flow amounts after the initial cash flow CF0.

CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000.

Note: See also irr(), here.

mod()	Catalog >
mod(Value1, Value2) ⇒ expression mod(List1, List2) ⇒ list mod(Matrix1, Matrix2) ⇒ matrix Returns the first argument modulo the second argument as defined by the identities: mod(x,0) = x mod(x,y) = x − y floor(x/y) When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument. If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements. Note: See also remain(), here

mod()

Catalog >

mod(Value1, Value2) ⇒ expression
mod(List1, List2) ⇒ list
mod(Matrix1, Matrix2) ⇒ matrix

Returns the first argument modulo the second argument as defined by the identities:

mod(x,0) = x
mod(x,y) = x − y floor(x/y)

When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument.

If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements.

Note: See also remain(), here

mRow()	Catalog >
mRow(Value, Matrix1, Index) ⇒ matrix Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Value.

mRow()

Catalog >

mRow(Value, Matrix1, Index) ⇒ matrix

Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Value.

mRowAdd()	Catalog >
mRowAdd(Value, Matrix1, Index1, Index2) ⇒ matrix Returns a copy of Matrix1 with each element in row Index2 of Matrix1 replaced with: Value • row Index1 + row Index2

mRowAdd()

Catalog >

mRowAdd(Value, Matrix1, Index1, Index2) ⇒ matrix

Returns a copy of Matrix1 with each element in row Index2 of Matrix1 replaced with:

Value • row Index1 + row Index2

MultReg	Catalog >
MultReg Y, X1[,X2[,X3,…[,X10]]] Calculates multiple linear regression of list Y on lists X1, X2, …, X10. A summary of results is stored in the stat.results variable. (See here.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

MultReg

Catalog >

MultReg Y, X1[,X2[,X3,…[,X10]]]

Calculates multiple linear regression of list Y on lists X1, X2, …, X10. A summary of results is stored in the stat.results variable. (See here.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.RegEqn	Regression Equation: b0+b1•x1+b2•x2+ ...
stat.b0, stat.b1, ...	Regression coefficients
stat.R2	Coefficient of multiple determination
stat.yList	yList = b0+b1•x1+ ...
stat.Resid	Residuals from the regression

MultRegIntervals	Catalog >
MultRegIntervals Y, X1[, X2[, X3,…[, X10]]], XValList[, CLevel] Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable. (See here.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

MultRegIntervals

Catalog >

MultRegIntervals Y, X1[, X2[, X3,…[, X10]]], XValList[, CLevel]

Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response.

A summary of results is stored in the stat.results variable. (See here.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Output variable	Description
stat.RegEqn	Regression Equation: b0+b1•x1+b2•x2+ ...
stat.y	A point estimate: y = b0 + b1 • xl + ... for XValList
stat.dfError	Error degrees of freedom
stat.CLower, stat.CUpper	Confidence interval for a mean response
stat.ME	Confidence interval margin of error
stat.SE	Standard error of mean response
stat.LowerPred, stat.UpperrPred	Prediction interval for a single observation
stat.MEPred	Prediction interval margin of error
stat.SEPred	Standard error for prediction
stat.bList	List of regression coefficients, {b0,b1,b2,...}
stat.Resid	Residuals from the regression

MultRegTests	Catalog >
MultRegTests Y, X1[, X2[, X3,…[, X10]]] Multiple linear regression test computes a multiple linear regression on the given data and provides the global F test statistic and t test statistics for the coefficients. A summary of results is stored in the stat.results variable. (See here.) For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

MultRegTests

Catalog >

MultRegTests Y, X1[, X2[, X3,…[, X10]]]

Multiple linear regression test computes a multiple linear regression on the given data and provides the global F test statistic and t test statistics for the coefficients.

A summary of results is stored in the stat.results variable. (See here.)

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

Outputs

Output variable	Description
stat.RegEqn	Regression Equation: b0+b1•x1+b2•x2+ ...
stat.F	Global F test statistic
stat.PVal	P-value associated with global F statistic
stat.R2	Coefficient of multiple determination
stat.AdjR2	Adjusted coefficient of multiple determination
stat.s	Standard deviation of the error
stat.DW	Durbin-Watson statistic; used to determine whether first-order auto correlation is present in the model
stat.dfReg	Regression degrees of freedom
stat.SSReg	Regression sum of squares
stat.MSReg	Regression mean square
stat.dfError	Error degrees of freedom
stat.SSError	Error sum of squares
stat.MSError	Error mean square
stat.bList	{b0,b1,...} List of coefficients
stat.tList	List of t statistics, one for each coefficient in the bList
stat.PList	List P-values for each t statistic
stat.SEList	List of standard errors for coefficients in bList
stat.yList	yList = b0+b1•x1+ . . .
stat.Resid	Residuals from the regression
stat.sResid	Standardized residuals; obtained by dividing a residual by its standard deviation
stat.CookDist	Cook’s distance; measure of the influence of an observation based on the residual and leverage
stat.Leverage	Measure of how far the values of the independent variable are from their mean values