cpr_coef: Estimated Coefficients of Constrained Polynomial Regression

In hzhang0311/lmcoef: Coefficients Estimation for Fitted Model

Description

The function cpr_coef is used to fit the following Polynomial Regression model with the parameter constraints and returns the estimated coefficients β's:

for i = 1,2,...,n,

Y_i = β_0 + ∑_{j=1}^p { β_j * (X_i) ^ j } + ε_i

ε_i ~ N(0,σ^2)

where coefficient β_j = β_{j-1} / j for j = 2,...,p, and predictor X_i = i / n

Usage

cpr_coef(p,y)

Arguments

p	A positive integer indicates the polynomial degree. Larger or equal to 2. NA is not allowed
y	A numeric vector that contains the true outcomes. NA is not allowed

Examples

p = 5
y = c(1,3,3,3,4,5,3,2,-1)

cpr_res = cpr_coef(p, y)

cpr_res$coefficients

#                 Estimate
# (intercept)  3.452393951
# b1          -1.100167971
# b2          -0.550083985
# b3          -0.183361328
# b4          -0.045840332
# b5          -0.009168066

cpr_res$residuals
# [1]  2.32310324  0.17861859  0.01715603 -0.16327333 -1.36488198 -2.59012461 -0.84171677 -0.12265344  2.56377227

cpr_res$fitted.values
# [1] 3.323103 3.178619 3.017156 2.836727 2.635118 2.409875 2.158283 1.877347 1.563772

hzhang0311/lmcoef documentation built on Dec. 20, 2021, 5:55 p.m.