# Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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### How can I get the 95% simultaneous confidence interval for four proportions?

300 male high school students are surveyed on their smoking frequencies, the results are following: Frequency (1)never smoke (2) 1-4/day (3) 5-10/day (4)more than 10/day Number of people ...
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### Inferring random variables from their sum

Suppose I have a large set of receipts that list the items I bought, but only list the total cost. One day I might have bought Milk, Butter, and Eggs. A different day I might have bought Bread, Milk,...
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### How to Use Chi-Squared Test for Inference about Three-way independence

If I recall correctly, three random variables X, Y, and Z are three-way independent iff these two statements are met: P(X∩Y∩Z) = P(X)P(Y)P(Z) X, Y, and Z are all pairwise independent of each other. ...
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### Calculate risk between classes

I am doing some exercises about logistic regression with SAS and I need to calculate and interpret odds. For calculating the individual probabilities I use those formulas: While later, the Professor,...
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### How time series structure can affect the independence of residuals condition for MLR?

I am going through all four conditions for Multiple Linear Regression and stick with this question: what happens with the independence if we have time series data structure?
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### How to compare two statistical distributions with unavailability measurements?

I have two different measuring instruments to evaulate if an electronic device is working or not. These instruments provide a working/not-working reading each day and at the end of the month I compute ...
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### Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
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### Testing equality of difference in coefficients from four regressions

This question is a follow-up/extension to this post. Suppose I have four regressions. $y_i=x_i\beta_i+\epsilon_i,\quad i=1,2,3,4$ I want to test whether $(\beta_1-\beta_2)-(\beta_3-\beta_4)>0$....
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### If a group is more likely to do something, does that mean that individuals in the group are more likely to do something?

I have some large amount of people take test A. Based on the scores on test A, I assign them either to group A1 or to group A2. A1 are the people with scores at least 50% on test A, and A2 has people ...
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### Interaction term to deal with heteroscedasticity

The variance in my dependent variable changes with a changing value in an important independent variable and is hence probably distorting the measured effect of the treatment. Can I combat this form ...
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### Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$

Given a random variable $X\sim Bin(n,p)$, where $p$ is known $p\in (0,1)$ , $n$ is an unknown positive integer and $x\in\{0,1,2,....n\}$, what is the maximum likelihood estimator of $n$? I ...
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### Conditional Expectation of Poisson

Suppose $X_1$,$X_2$,$X_3$,.....,$X_n$ are i.i.d. random variables with a common pmf poisson(λ) (t = a value) How would you calculate the below without using intuition (I would appreciate if you ...
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### model for regression with restricted dependent and independent variables

I am working on grade prediction. I have previous grades from the students and am planning to predict their future scores. Both past and future test scores are restricted from 0 - 15. When i run ...
### How to infer the parameter $p = f(n)$ of different Bernoulli distributions $X_{n}$?
I have a dataset corresponding to the results of independant Bernoulli trials. Each trial is associated to a number $n \in ]1;+\infty[$ and follows a Bernoulli distribution with parameter \$p=f(n)=b + ...