multiple linear regression with 5 records and 25 features

Question

           X1     X2    X[...]    X25    Y 

Q1_2019    23     65    18        32     1,6  
Q2_2019    87     32    23        46     1,2  
Q3_2019    34     15    63        78     3,2  
Q4_2019    85     45    43        65     3,9  
Q1_2020    85     43    78        35     1,1  
Q2_2020    37     78    54        78     1,5  

• I have a very expensive dataset which shows aggregated survey data. These are probably means. I am trying to get the individual data but at the moment that is all I have.
• The shape of data frame is 5x26
• Y data so far is collected data calculated at the end of each quarter via other means The survey is done at the beginning of the quarter.
• Y is my dependent variable and I would like to derive a polynom to predict the exact number based on future X data or at least the probable trend it will be going in the next quarter once new survey data is available. Up, down, stable would be enough
• I have done correlation analysis (all vs all) and there are strong pairwise correlation between several X and Y

Questions

1. Y comes as a one digit before the comma and one digit after the comma. Since all other values are 2 digits before the comma I would like to multiply it with 10 to transform it into 2 digits before the comma.Is that ok from math/data science perspective?
2. 5 records is not much but there are a lot of features. I would like to do multiple linear regression. Do you think this feasible with this data set? What would be objections and risks doing that?
3. Would upsampling the dataset help me with anything here? Or could I just work with the five records?
4. With the strange shape of the dataset especially the low number of records do you think that sufficient precision can be reached?
5. How could I calculated the maximum possible precision/discriminative power possible with this dataset? (I am looking for strong arguments why they should give me access to the complete dataset)

Answer 1

1. Y comes as percent in the format. To put it into the same dimension as X I multiplied it with 10. Is that ok from math/data science perspective?

As far as I can tell there's no reason to do that, and why multiply by 10?

2. 5 records is not much but there are a lot of features. I would like to do multiple linear regression. Do you think this feasible with this data set? What would be objections and risks doing that?

The fact that there are lots of features makes it harder to work with few instances, not easier. There is a very high risk of overfitting, that is of the model catching patterns which appear by chance in the features. This leads to predictions being also affected by chance, so bad performance.

3. Would upsampling the dataset help me with anything here? Or could I just work with the five records?

Upsampling is unlikely to work since it's going to reproduce the patterns in the small dataset, so it's also going to reproduce patterns which appear by chance.

4. With the strange shape of the dataset especially the low number of records do you think that sufficient precision can be reached?

It depends what the data represents, if the features happen to be really good predictors for the dependent variable and are not affected by chance, it might work. But these are very optimistic assumptions, in general it's not reasonable to expect good predictions from such a small set of instances.

5. How could I calculated the maximum possible precision/discriminative power possible with this dataset? (I am looking for strong arguments why they should give me access to the complete dataset)

In general I would suggest doing a leave-one-out experiment: use 4 instances as training set, 1 instance as test set, repeat 5 times with a different instance as test set every time. Measuring the average performance should give you an idea how far off the predictions are going to be (you could use a very simple evaluation measure such as mean absolute error).

However what you have is actually a time series apparently, so it might be worth looking at methods which take time evolution into account.

Answer 2

Meaningful multiple linear regression can not performed with just 5 samples.

With only 5 samples, a case study approach would be more appropriate.