It is with great pleasure that I can announce that Ryacas version 1.1.0 has now been accepted into Journal of Open Source Software and same version released to CRAN. (The source code is available at https://github.com/mikldk/ryacas/.)
I already wrote about Ryacas many times before. I will refer you to the “Getting started” and “The high-level (symbol) interface” vignettes or one of the others available at the CRAN page or the package’s website.

It is with great pleasure that I can announce that Ryacas version 1.0.0 is now released to CRAN (https://cran.r-project.org/package=Ryacas). I wish to thank all co-authors: Rob Goedman, Gabor Grothendieck, Søren Højsgaard, Grzegorz Mazur, Ayal Pinkus.
It means that you can install the package by (possible after binaries have been built):
install.packages("Ryacas") Followed by:
library(Ryacas) (The source code is available at https://github.com/mikldk/ryacas/.)
Now you have the yacas computer algebra system fully available!

In a recent blog post I tried to get yacas to solve a system of polynomial equations. Unfortunately it could not do that, so I solved it numerically instead. Now it is possible – together with many other systems of polynomial equations thanks to fixing a small error in yacas. It has now been fixed, also in Ryacas (development version), so hurry up and update Ryacas to the latest version 0.

Finding prediction intervals (for future observations) is something different than finding confidence intervals (for unknown population parameters).
Here, I demonstrate one approach to doing so.
First we load the library and simulate some data:
library(mgcv) set.seed(1) dat <- gamSim(eg = 1, n = 400, dist = "normal", scale = 2) ## Gu & Wahba 4 term additive model The simulated in dat contains the “truth” in the f variables:

In a recent blog post I used something like this (for use in a call to optim()):
obj_fun_expr <- expression((x^4 + 4 * x^2 * y^2 - 12 * x^2 * a + 144 * x^2 - 48 * x * y * a + 144 * x * y - 4320 * x + 36 * y^2 - 2160 * y + 180 * a^2 + 32400)/16) f_expr <- function(par) { x <- par[1] y <- par[2] a <- par[3] val <- eval(obj_fun_expr, list(x = x, y = y, a = a)) return(val) } I have been wondering what the cost of eval(expr, .

Let \(\rho_{XY}\) be the correlation between the stochastic variables \(X\) and \(Y\) and similarly for \(\rho_{XZ}\) and \(\rho_{YZ}\). If we know two of these, can we say anything about the third?
In a recent blog post I dealt with the problem mathematically and I used the concept of a partial correlation coefficient. Here I will take a simulation approach.
First z is simulated. Then x and y is simulated based on z in a regression context with a slope between \(-1\) and \(1\).

It is important to test software. One approach is unit-testing, and for R packages this can e.g. be done using testthat.
It is also important to document software. For R packages roxygen2 is really helpful: It enables you to write documentation in the code file in the R/ folder where the function is implemented. And then roxygen2 takes care of handling the Rd files in the man/ folder.
I have made a new R package that combines these approaches: roxytest.

Update Aug 10, 2019: I wrote a new blog post about the same as below but using a simulation approach.
Update Aug 27, 2019: Minor change in how equations are solved (from version 0.9.0.9122).
Let \(\rho_{XY}\) be the correlation between the stochastic variables \(X\) and \(Y\) and similarly for \(\rho_{XZ}\) and \(\rho_{YZ}\). If we know two of these, can we say anything about the third?
Yes, sometimes, but not always.

Update Aug 27, 2019: I wrote a new blog post showing that Ryacas can now solve the system of equations directly without using optim().
As you may know, I am maintaining the Ryacas package (with online documentation) for doing symbolic mathematics (and other stuff) in R using the yacas software (with online documentation).
Søren Højsgaard and I have been preparing a new major release of Ryacas (see blog post on it).

I am learning how to play piano. In that process, I needed charts with piano chords. I know it is good practise to construct the chords manually, figure out the inversions and so on, but I found that some aspects of learning were improved with a chord chart. I searched the (entire!) internet, and struggled to find good, customisable charts.
Thus I had to make something myself: pichor, an R package for making and working with piano chords in R.

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