I have two separate problems. One is logistic regression and other is time series prediction. But both suffer from paucity of data problems
a) For logistic regression, I have tiny dataset with 10 observations which has variables such as age, Marital_Status, income, gender and car_purchase_status (outcome flag with Yes/No values). Now I have a new 11th customer with variables such as Age, gender, Marital_Status and income. Now I would like to know whether this 11th customer will buy a car or not. Should I spend resources to influence him to buy a car? Am I spending my resources on the right customer? For ex: Is there anyway that I can find out that 11th customer has 70% or 80% pc chance of buying a car. So spending some marketing efforts such as calls can help us convince him to buy a car (100%). So, how can I do this? Any advice please? Should I just give up straight away that this problem impossible to solve with such low data or is there any simple statistical techniques that can help me gain some insights about 11th customer?
b) For time series, I have only 10 observations each spaced at 20 days gap. For ex: I have their revenue generated for day1,day21,day41,day61,day81.....day201. Now with the given 10 observations, I would like to predict the revenue generated for day500, day321, day621 etc. So, is it possible to run time series forecasting with such short series? Can you guys guide me on this please? Here, also should I give up because of low data points or is there any methods that I can use to predict the future timestamp points based on short input time series?
Can you guys please help me with list of steps/topics that can help me do this?