# regression with percentage DV and multiple dummy IV

I am running a market analysis about e-mail responses for my marketing class.

I have the following data entries:

Observations: 400 different sequences of e-mails where sent to different target groups. Each sequence has a different number of delivered emails (from a batch of 18 to 70 e-mails), each has a different reply rate, number of positive answers, and conversion rate.

I have the following dummy variables:

1. Country of focus (i.e. 5 different countries where e-mails are sent)
2. Different call to actions (i.e. call, appointment, demonstration)
3. 1 external factor (i.e. holiday or normal working day)
4. Seniority level of the target (i.e. management, employee, intern)

I want to know which IV may/may not have an impact on the number of positive replies and conversion rate.

After numerous readings and videos, I did not find an answer about how to run regression using percentage dependent variable(s) and multiple dummies.

Note1: Reply/delivered are defined as percentage of number of delivered emails (i.e. 5% out of 35 delivered emails) Note2: Reply rates are defined as percentage of total number of replies (i.e. 1.47% of all replies are for sequence 15 out of 19 sequences)

See an excerpt of data in attached file.

• Do you only have percentages? or do you have the numerator/denominator? It would be better to use data in the last form, then maybe poisson regression with $\log(\text{denominator})$ as an offset. Search this site for poisson-regression. – kjetil b halvorsen Dec 27 '18 at 15:39
• If you have numerator and denominator, then binomial regression. If not, fractional logistic regression, or, if there are no 0 or 100% response rates, beta regression. But you can find more discussion elsewhere on CV. – The Laconic Dec 29 '18 at 4:04