wslr

Syntax

wslr(Y, X, W, [mse=false])

Arguments

Y is a numeric vector indicating the dependent variable.

X is a numeric vector indicating the independent variable.

W is a numeric vector indicating the weights, where all elements are non-negative.

The length of Y, X and W must be equal.

mse (optional) is a Boolean scalar specifying whether to output the mean squared error (mse). The default value is false.

Details

wslr (weighted single linear regression) calculates the weighted linear regression of Y on X.

Return value: A tuple, containing the intercept alpha, regression coefficients beta, and mean squared error mse (if mse set to true).

where n is the number of non-empty values.

Comparing wls and wlsr:

• wls returns a vector, while wslr returns a tuple.

• wls is a vector function, while wslr is an aggregate function.

• Only wls can be applied to DFS tables.

Examples

x = [0.78,0.38,0.2,0.52,0.12,0.49,0.02,0.67,0.94,0.85]
y = [0.11,0.63,0.19,0.36,0.02,0.35,0.98,0.07,0.55,0.43]
w = [0.05665,0.155172,0.142857,0.236453,0.125616,0.061576,0.064039,0.051724,0.004926,0.100985]
wslr(y,x,w)
//output: (0.385342531009792,-0.076256407696962)
wslr(y,x,w,true)
//output: (0.385342531009792,-0.076256407696962,0.007842049148797)

Since wls is a vector function, it cannot be directly used with moving but requires a user-defined function. wlsr, on the other hand, can be directly combined with moving.

s = ["001","002","003","004","005","006","007","008","009","010"]
y = [0.2531,0.5672,0.8347,0.6436,0.699,0.3732,0.0676,0.9129,0.0167,0.755]
x = [0.5782,0.8064,0.5035,0.7857,0.5955,0.4156,0.7609,0.093,0.6504,0.9092]
w = [0,0.095909021199675,0.195930114343433,0.300024080233914,0.408136784222979]

t = table(s,y,x)
select moving(wslr{,,w,true},[y,x],5,5) as `alpha`beta`mse from t