Poisson Regression vs. Linear Regression

Linear regression comes with its own set of modeling challenges.

For instance:
- It cannot model count (or discrete) data.
- After modeling, the output can be negative. This may not make sense at times — predicting the number of goals scored, number of calls received, etc.

Furthermore, in linear regression:
- Residuals are expected to be normally distributed around the mean.
- Hence, outcomes on either side of the mean (m-x, m+x) are equally likely.

For instance:
- if the expected number (mean) of calls received is 1...
- ...then, according to linear regression, receiving 3 calls (1+2) is just as likely as receiving -1 (1-2) calls.
- This does not make any sense.

Thus, if the above assumptions don't hold, linear regression won't help.

Instead, what you may need is Poisson regression.

Poisson regression:
- is more suitable if your response (or outcome) is count-based.
- assumes that the response comes from a Poisson distribution.

Contrary to linear regression, in Poisson regression:
- Residuals may follow an asymmetric distribution around the mean (λ).
- Hence, outcomes on either side of the mean (λ-x, λ+x) are NOT equally likely.

For instance:
- if the expected number (mean) of calls received is 1...
- ...then, according to Poisson regression, it is possible to receive 3 (1+2) calls, but it is impossible to receive -1 (1-2) calls.
- This is because its outcome is also non-negative.