wls

wls(Y, X, W, [intercept=true], [mode=0])

Y is a dependent variable.

X is an independent variable.

Y is a vector. X can be a matrix, table or tuple. When X is a matrix, if the number of rows is equal to the length of Y, each column of X is a factor. If the number of rows is not equal to the length of Y, but the number of columns is equal to the length of Y, each row of X is a factor.

W is a vector indicating the weight in which each element is a non-negative.

intercept (optional) is a Boolean variable that indicates whether to include the intercept in regression. The default value is true. When it is true, the system automatically adds a column of "1" to X to generate the intercept.

mode (optional) is an integer that could be 0, 1, or 2.

• 0: a vector of the coefficient estimates

• 1: a table with coefficient estimates, standard error, t-statistics, and p-value

• 2: a dictionary with all statistics

ANOVA (one-way analysis of variance)

RegressionStat (Regression statistics)

Coefficient

Residual: the difference between each predicted value and the actual value.

Return the result of an weighted-least-squares regression of Y on X.

x1=1 3 5 7 11 16 23
x2=2 8 11 34 56 54 100
y=0.1 4.2 5.6 8.8 22.1 35.6 77.2;
w=rand(10,7)
wls(y, x1, w)

// output
[-17.6177  4.0016]

wls(y, (x1,x2), w);

// output
[-17.4168  3.0481 0.2214]

wls(y, (x1,x2), w, 1, 1);

wls(y, (x1,x2), w,1, 2);

// output
Coefficient->
factor    beta      stdError tstat     pvalue
--------- --------- -------- --------- --------
intercept -10.11392 4.866583 -2.078239 0.106234
x1        3.938138  2.061191 1.910613  0.128655
x2        -0.088542 0.446667 -0.198227 0.852534

Residual->[6.452866,3.207839,-3.002812,-5.642629,-6.147264,-12.515038,5.590914]
RegressionStat->
item         statistics
------------ ----------
R2           0.957998
AdjustedR2   0.936997
StdError     17.172833
Observations 7

ANOVA->
Breakdown  DF SS           MS           F         Significance
---------- -- ------------ ------------ --------- ------------
Regression 2  26905.306594 13452.653297 45.616718 0.001764
Residual   4  1179.624835  294.906209
Total      6  28084.931429

x=matrix(1 4 8 2 3, 1 4 2 3 8, 1 5 1 1 5);
w=rand(8,5)
wls(1..5, x,w,0,1);