Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [inverse-prediction]

Predicting an explanatory variable from an observation of the dependent variable, also called inverse regression or calibration.

See https://en.wikipedia.org/wiki/Calibration_(statistics) which also covers other uses of the terms, and https://psychologydictionary.org/inverse-prediction/

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How to calculate the confidence interval of the x-intercept in a linear regression?

Since standard error of a linear regression is usually given for the response variable, I'm wondering how to obtain confidence intervals in the other direction - e.g. for an x-intercept. I'm able to visualize what it might be, but I'm sure there…
Marc in the box
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How to do 4-parametric regression for ELISA data in R

I am a biology student. We do many Enzyme Linked Immunosorbent Assay (ELISA) experiments and Bradford detection. A 4-parametric logistic regression (reference) is often used for regression these data following this function: $$ F(x) =…
kaji331
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Error bars, linear regression and "standard deviation" for point

I have a set of experimental data points. I performed the measurements in triplicate, for each of the point of the data set. Therefore, I can draw each data point with the standard deviation of each triplicate. See the picture attached. In…
Rififi
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If X can predict Y in regression, why isn't Y guaranteed to predict X?

Intuitively, if X can predict Y in a multiple linear regression model, $y$ = $\beta_0$ + $\beta_1$$X$ + $\beta_2$$Z$ + $e$ X and Y are associated. Since there's an association between them, why is it not guaranteed that I could predict X by Y? Why…
JetLag
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linear model, given y, calculate the confidence interval for x

I fit the model y = a + b * x. And 95% CI for estimates of a and b are (a1, a2), (b1, b2), respectively. If we have a new observation x0, then the estimated response is a_hat + b_hat * x0. And the 95% CI is (a1 + b1 * x0, a2 + b2 * x0) Case 1, now…
OMG
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Inverse Regression vs Reverse Regression

I'm aware there's a great number of questions which deal with the mathematical difference between the two, but I'm still confused as to best practice. Basically I'm looking at a situation where we have lots of bad data, and some good data (which we…
JackEm
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inverse.predict chemcal package

I have noticed that the inverse.predict function (chemCal package) does not take into account all the degrees of freedom of the model in order to calculate the confidence interval, and I am wondering why. Let me explain a bit better. I was trying…
AnnaB
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Confidence interval for vertex of quadratic model, transforming parameters estimated by MLE

If I have a model $y=ax^2+bx+c+\epsilon$, and I use maximum likelihood estimation (in R, with nlm function) to estimate $(a,b,c)$ with a Hessian matrix $H$ as a results, can I use this to calculate the (95%) C.I. for the $x$-coordinate of the vertex…
breezeintopl
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Confidence interval from two methods

I have some data in the form of (x,y) tuples, 50 tuples. I am trying to fit a quadratic so y = ax^2+bx+c My goal is to find the max of the quadratic, so max = -b/2a and also find the confidence interval around that. I find the max after fitting…
gbh.
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Inverse Predictive Posterior

Suppose I have a parametric nonlinear model, say $$ y_i |\theta \sim N(f_{\theta}(x_i), \sigma^2) $$ with known form of $f_\theta$. We get data $d=(y_i,x_i)_{i=1,\ldots,n}$ and obtain posterior samples so we can make inference on $\theta|d$. This…
bdeonovic
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Should I use the prediction interval or inverse prediction interval to calculate the uncertainty of $x$ when using reverse regression?

I'm calibrating a piece of lab instrumentation. I create solutions of known concentration ($x$) and measure my instrument response ($y$). On unknown samples, I measure the response and use the regression line to predict the actual concentration…
Kevin Nowaczyk
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Neural Network Inversion and its consequences

I am currently looking at Federated Learning. Here is a good example from google. The idea is that training happens on multiple devices. This means on one hand that training data never leaves a user (privacy) and on the other hand that it can be run…
Mr.Sh4nnon
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How do I predict subject mean (w/ error) with repeated measurements in SPSS?

Context: say I am trying to determine the concentration of a chemical, so I take known concentrations of the chemical and make a standard curve (6 measurements per standard) then measure my unknown 6 times. Here's what I can do: I can use linear…
DocBuckets
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Why inverse of 'predict' function in R can not be used for dependent variable prediction in linear model?

When a regression is calculated with a simple linear model that returns intercept and slope for an equation like this $y=a + bx$ one can predict $y$, the response variable, based on that equation. Equally one could rearrange for $x$:…
USER_1
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Which is the error of a value corresponding to the maximum of a function?

This is my problem: I use data observed with MUSE (which is an astronomical instrument provides cubes, i.e. an image for each wavelength with a certain range, link ) to extract a measure of redshift. Let's call the MUSE cube with $S_{ij}$, where $i$…
Giuseppe Angora
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