LORs in Math/Stat

[kingduck]

Hi guys, this is about LOR strategy in the math/stat space, and I thought it might be helpful to have my profile attached as well. I wanted to know what the best strategies for getting letters of recommendations are. While I have been through the LOR process for the masters applications, I wanted to take a more nuanced approach this cycle.

As mentioned previously, I have 1 professor (call him professor X) from my masters program with whom I took 2 classes with and we are currently working on 2 research topics, one on time series and one on COVID data analysis. Another professor (call him professor Y), I have also taken 2 classes with: in mathematical stats and survival analysis. I am hoping to receive good letters from them, but what should I ask them to emphasize on (or what is an appropriate way to ask them to talk about my research/math ability)?

My plan is the following:

• Professor X: ask to speak to my research ability
• Professor Y: ask to speak to my mathematical stats ability - i have discussed with him some research methodology (regarding the work with professor X) but not extensively

I have three more professors I am considering, a marketing professor from my undergrad with whom I did some text analysis with (call him Professor Q, and wrote my letter for my masters application), a stats professor from my grad program with whom I got an A in his multivariate stats class (call him professor R), and my real analysis professor (call him Professor S, who is a math lecturer at Harvard). 

• Professor Q: really nice guy, think he will write a letter that speaks to research and data analysis ability, like he did before
• Professor R: unsure - I also spoke a little about potential research in multivariate stats with him (nothing became of it), probably an average recommendation along the lines of "good at linear algebra/math"
• Professor S: lecturer at Harvard, found one of his letters online and seemed to be rather uninformative (student scored 98% on exam 1 etc..., we covered materials XYZ from textbook by Professor so and so.)

My questions really can be summed up as the following:

1. What type of letters should I aim for? Should they say how good of a student I am, or how good of a researcher I am?
2. Should I even consider professors R or S, since their letters are anticipated to be pretty average?
3. It seems like a no-brainer, that I should ask professor Q, since he can speak to my research ability, but will the fact that he's from the marketing department somehow make what he has to say about me weigh a little "less?" 
4. What is the most appropriate way to ask a professor to write about, say, research ability, or math ability?

I'd appreciate any advice on LOR strategy