[Statistics] Interview Questions

1. Assumptions of OLS

- The relationship between X and Y is linear

- Y is distributed normally at each value of X

- The variance of Y at every value of X is the same (homogeneity of variances)

- The observations are independent

2. Assumptions of logistic regression
- Binary logistic regression requires the dependent variable to be binary and ordinal logistic regression requires the dependent variable to be ordinal. The categories (groups) must be mutually exclusive and exhaustive; a case can only be in one group and every case must be a member of one of the groups.
- The model should be fitted correctly.  Neither over fitting nor under fitting should occur.  That is only the meaningful variables should be included, but also all meaningful variables should be included.  
- The error terms need to be independent.  Logistic regression requires each observation to be independent. 
- Logistic regression assumes linearity of independent variables and log odds. Logistic regression does not assume a linear relationship between the dependent and independent variables.
- Lastly, it requires quite large sample sizes.  Because maximum likelihood estimates are less powerful than ordinary least squares (e.g., simple linear regression, multiple linear regression); whilst OLS needs 5 cases per independent variable in the analysis, ML needs at least 10 cases per independent variable, some statisticians recommend at least 30 cases for each parameter to be estimated.
- For a binary regression, the factor level 1 of the dependent variable should represent the desired outcome.
- No normal distribution, no equal variance

3. Multicollinearity- Multicollinearity arises when two variables that measure the same thing or similar things (e.g., weight and BMI) are both included in a multiple regression model; they will, in effect, cancel each other out and generally destroy your model.