regression

I am trying to obtain estimated constrained coefficients using RSS. The beta coefficients are constrained between [0,1] and sum to 1. Additionally, my third parameter is constrained between (-1,1). Utilizing the below I can obtain a nice solution using simulated variables but when implementing the methodology on my real data set I keep arriving at a non-unique solution. In turn, I'm wondering if there is a more numerically stable way to obtain my estimated parameters. set.seed(234) k = 2 a = diff(c(0, sort(runif(k-1)), 1)) n = 1e4 x = matrix(rnorm(k*n), nc = k) a2 = -0.5 y = a2 * (x %*% a) +

Assuming we have the below function to optimize for 4 parameters, we have to write the function as below, but if we want the same function with more number of parameters, we have to rewrite the function definition. def radius (z,a0,a1,k0,k1,): k = np.array([k0,k1,]) a = np.array([a0,a1,]) w = 1.0 phi = 0.0 rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1) return rs The question is if this can be done easier in a more automatic way, and more intuitive than this question suggests. example would be as following which has to be written by hand. def radius (z,a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,k0,k1,k2

(reproducible example given) In the following, I get an abline line with y-intercept is about 30, but the regression says y-intercept should be 37.2851 Where am I wrong? mtcars$mpg # 21.0 21.0 22.8 ... 21.4 (32 obs) mtcars$wt # 2.620 2.875 2.320 ... 2.780 (32 obs) regression1 <- lm(mtcars$mpg ~ mtcars$wt) coef(regression1) # mpg ~ 37.2851 - 5.3445wt plot(mtcars$mpg ~ mtcars$wt, pch=19, col='gray50') # pch: shape of points abline(h=mean(mtcars$mpg), lwd=2, col ='darkorange') # The y-coordinate of hor'l line: 20,09062 abline(lm(mtcars$mpg ~ mtcars$wt), lwd=2, col ='sienna') I looked at all the

I would like to make a regression tree like the one in the picture. The tree was done in Cubist but I don't have that program. I do use R and Python. It seems to differ from the R packages rpart or tree in that the end nodes are linear formulas rather than just the average value. Is there any way I can do this using R or some other free software? In the picture, NDVI, B1,B2, etc are variables. The image is from this website . Cubist is an R port of the Cubist GPL C code released by RuleQuest at http://rulequest.com/cubist-info.html . Using the example from help('cubist') and the original

The dataset I would like to analyse looks like this n <- 4000 tmp <- t(replicate(n, sample(49,6))) dat <- matrix(0, nrow=n, ncol=49) colnames(dat) <- paste("p", 1:49, sep="") dat <- as.data.frame(dat) dat[, "win.frac"] <- rnorm(n, mean=0.0176504, sd=0.002) for (i in 1:nrow(dat)) for (j in 1:6) dat[i, paste("p", tmp[i, j], sep="")] <- 1 str(dat) Now I would like to perform a regression with depended variable win.frac and all other variables ( p1 , ..., p49 ) as explanatory variables. However, with all approaches I tried I get the coefficient for p49 as NA, with the message "1 not defined

A simple question I hope. I have an experimental design where I measure some response (let's say blood pressure) from two groups: a control group and an affected group, where both are given three treatments: t1, t2, t3. The data are not paired in any sense. Here is an example data: set.seed(1) df <- data.frame(response = c(rnorm(5,10,1),rnorm(5,10,1),rnorm(5,10,1), rnorm(5,7,1),rnorm(5,5,1),rnorm(5,10,1)), group = as.factor(c(rep("control",15),rep("affected",15))), treatment = as.factor(rep(c(rep("t1",5),rep("t2",5),rep("t3",5)),2))) What I am interested in is quantifying the effect that each