regression

I have a correlation plot for two variables, the predictor variable (temperature) on the x-axis, and the response variable (density) on the y-axis. My best fit least squares regression line is a 2nd order polynomial. I would like to also plot confidence and prediction intervals. The method described in this answer seems perfect. However, my dataset (n=2340) has repeated entries for many (x,y) pairs. My resulting plot looks like this: Here is my relevant code (slightly modified from linked answer above): import numpy as np import pandas as pd import matplotlib.pyplot as plt from statsmodels

Let's say that I have a numeric data matrix with columns w, x, y, z and I also want to add in the columns that are equivalent to w*x, w*y, w*z, x*y, x*z, y*z since I want my covariate matrix to include all pairwise interactions. Is there a clean and effective way to do this? If you mean in a model formula , then the ^ operator does this. ## dummy data set.seed(1) dat <- data.frame(Y = rnorm(10), x = rnorm(10), y = rnorm(10), z = rnorm(10)) The formula is form <- Y ~ (x + y + z)^2 which gives (using model.matrix() - which is used internally by the standard model fitting functions) model.matrix

I'm trying to learn QR decomposition, but can't figure out how to get the variance of beta_hat without resorting to traditional matrix calculations. I'm practising with the iris data set, and here's what I have so far: y<-(iris$Sepal.Length) x<-(iris$Sepal.Width) X<-cbind(1,x) n<-nrow(X) p<-ncol(X) qr.X<-qr(X) b<-(t(qr.Q(qr.X)) %*% y)[1:p] R<-qr.R(qr.X) beta<-as.vector(backsolve(R,b)) res<-as.vector(y-X %*% beta) Thanks for your help! setup (copying in your code) y <- iris$Sepal.Length x <- iris$Sepal.Width X <- cbind(1,x) n <- nrow(X) p <- ncol(X) qr.X <- qr(X) b <- (t(qr.Q(qr.X)) %*% y)[1:p]

I'm using a set of points which go from (-5,5) to (0,0) and (5,5) in a "symmetric V-shape". I'm fitting a model with lm() and the bs() function to fit a "V-shape" spline: lm(formula = y ~ bs(x, degree = 1, knots = c(0))) I get the "V-shape" when I predict outcomes by predict() and draw the prediction line. But when I look at the model estimates coef() , I see estimates that I don't expect. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.93821 0.16117 30.639 1.40e-09 *** bs(x, degree = 1, knots = c(0))1 -5.12079 0.24026 -21.313 2.47e-08 *** bs(x, degree = 1, knots = c(0))2 -0

A newbie question: does anyone know how to run a logistic regression with clustered standard errors in R? In Stata it's just logit Y X1 X2 X3, vce(cluster Z) , but unfortunately I haven't figured out how to do the same analysis in R. Thanks in advance! David F You might want to look at the rms (regression modelling strategies) package. So, lrm is logistic regression model, and if fit is the name of your output, you'd have something like this: fit=lrm(disease ~ age + study + rcs(bmi,3), x=T, y=T, data=dataf) fit robcov(fit, cluster=dataf$id) bootcov(fit,cluster=dataf$id) You have to specify x=T

When doing regression or classification, what is the correct (or better) way to preprocess the data? Normalize the data -> PCA -> training PCA -> normalize PCA output -> training Normalize the data -> PCA -> normalize PCA output -> training Which of the above is more correct, or is the "standardized" way to preprocess the data? By "normalize" I mean either standardization, linear scaling or some other techniques. Chris Taylor You should normalize the data before doing PCA. For example, consider the following situation. I create a data set X with a known correlation matrix C : >> C = [1 0.5; 0

I have a problem which deals with predicting two outputs when given a vector of predictors. Assume that a predictor vector looks like x1, y1, att1, att2, ..., attn , which says x1, y1 are coordinates and att's are the other attributes attached to the occurrence of x1, y1 coordinates. Based on this predictor set I want to predict x2, y2 . This is a time series problem, which I am trying to solve using multiple regresssion. My question is how do I setup keras, which can give me 2 outputs in the final layer. I have solved simple regression problem in keras and the code is avaialable in my github