I can't speak for engineering but I'm typically the hiring manager for entry data scientist. Based on what you are telling me right now, there does not exist a reason why I would hire you to be a data scientist for me.
- SQL + some high level language: I need to know that you can a)Perform complex joins b)Integrate the workflow into an automatic process such that the pulling of data and the implementation model are seamless. Good news is that this is relatively easy to learn. I recommend you learn python and utilize sqlaclehmey and pandas to incorporate queries, data cleaning and data modeling into one program. Having this knowledge makes you much more interesting to me.
- Statistical Knowledge: If I ask you make a model that predicts if product A is defective can you do this? If I ask you to predict the number of calls into our call centers can you do this? Do you know when to use a classifier or a regression? Can you do a time series analysis? If you don't have this skill set at all, then why would I bother interviewing you?
- P-value: Tell me what it is in a non-technical way and tell me the limits. Tell me how a support vector machine works without using linear algebra.
- Agile: This is non-technical but being familiar with the terms "sprint", "user story" and "iterations" within an agile framework is always a good thing.
- Data validation: Let's say you have built a program that pulls data from a database and makes a model. You have automated this. What kind of checks will you build into your program that will let you know if the data from the database is not flawed in some way.
What I have listed above are the baseline I have for new hires. Notice that none of this references actually work experience, it's simply knowledge that needs to be expressed on a resume and during an interview. If you don't have any of this on your resume, then I have no incentive to interview you. If you can't articulate your thought process on this during an interview, I have no incentive to hire you.
Now with that said. A lot of this can gained relatively easily, but it takes time on your part to acquire this skills. Udacity, Cousera and Kaggle competitions can help you become a more interesting candidate in my mind.
My advice is leverage your ability to translate technical issues into simple terms. I've interviewed highly trained PhD's who failed explaining to my non-technical peer their model in a simple terms. In fact, my last interview I gave was this case exactly. One candidate was a PhD from a top 20 university who has done research in neuroscience, the other was an undergraduate in statistics from a top 20 school too. The PhD had a lot of appealing skills, but he couldn't convey his work at a high level, he got too caught up in the jargon. While the undergraduate lacked a lot of the more advance knowledge across the board, and computer science skills (he knew enough though), he did really well explaining everything he knew. He would draw pictures, use jargon, but then break it down in easy to digest terms. That is a rare skill and why I hired him instead.