The assumptions of multinomial and linear regression analysis are as follows:

Assumptions of Multinomial Regression Analysis:

Assumptions of Linear Regression Analysis:

Thanks.

Unfortunately the linearity assumption was misstated. The linearity assumption is that the prediction equation is a a linear transformation in the sense of matrix algebra between the DV and any and all IVs. Further multicollinearity was somewhat misstated. Here the problems can arise if there is less than perfect correlation between the IVs. See Kutner et al .APPLIED LINEAR STATISTICAL MODELS 5ed for details. Best wishes, David Booth

The Multinomial logistic regression is a statistical test that involves a single category variable which is predicted using one or more other factors. This method also establishes the numerical relation between such variable pairs. A categorical variable should be your targeted predictor. Linearity, independence, and the absence of outliers and multicollinearity are among the assumptions for multinomial logistic regression. For the details related to assumptions of multinomial logistic regression you may refer to following link:

https://www.statstest.com/multinomial-logistic-regression/

A linear relationship, zero conditional mean of the error terms, Gaussian distribution of the error terms, homoskedasticity of the error terms, the absence of outliers, multicollinearity, and autocorrelation of the error terms are among the assumptions for linear regression. For more details you may use the following link:

https://www.geeksforgeeks.org/assumptions-of-linear-regression/

Hope this would be useful.

A less detailed approach to the assumptions is to say that your analysis is attempting to describe the conditional distribution of the dependent variable given the independent variables and how this varies as the independent variables change. The assumptions are doing two things: (a) imposing a strong structure on that possible change; (b) allowing some statistical inferences to be made, in terms of uncertainty of estimates and significance testing.