Ideally, the observed data should have the sample mean equal to the sample variance (or close to one another except for randomness) in order for the Poisson Regression model to be appropriate for that data. If the observed count data for a sample has a variance that is larger than the sample mean, it is said to be over dispersed.

Question

Ideally, the observed data should have the sample mean equal to the sample variance (or close to one another except for randomness) in order for the Poisson Regression model to be appropriate for that data.  If the observed count data for a sample has a variance that is larger than the sample mean, it is said to be over dispersed.

BlackTom AI · Accepted Answer

The question discusses a property of Poisson regression and when it is appropriate to use this model. 
Option 1: True. In a Poisson distribution, the mean and the variance are equal (both equal to the rate parameter λ). Therefore, for Poisson regression to be appropriate, the observed data should exhibit roughly equal sample mean and sample variance, allowing for randomness. When the observed variance is larger than the mean, this is termed overdispersion, which suggests that the Poisson assumption (mean equals variance) is violated and alternative models (like negative binomial) may be more suitable. 
Option 2: False. If one assumes Poisson regression and observes overdispersion (variance greater than the mean), the statement that Poisson is appropriate is not supported. The presence of overdispersion indicates a mismatch between the data and the Poisson assumptions, making False an incorrect stance in this context. 
To summarize the core idea: the Poisson model implies mean equals variance, so equal or near-equal sample mean and variance is desirable; overdispersion (variance > mean) signals potential model misspecification for Poisson rather than suitability. Hence the true description is that observed overdispersion contradicts Poisson appropriateness, reinforcing why the True option aligns with the underlying theory.

2025WI_MSDS_410-DL_SEC56 Quiz #5: Poisson and ZIP Regression

View Explanation

Log in for full answers

Similar Questions

Poisson Regression uses a logistic transformation on Y so that a linear model can be used on the transformed data.

Poisson regression is a type of Generalized Linear Model.

A Poisson model is a good choice of regression model in which of the following situations:

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler