The influence of the correlation among independent variables on the slope

[GoulsonWang]

Hi,

Thank you for providing such a useful normalization tool !

However, When I was reviewing the paper, I found that the degree d was considered in the second quantile regression. Obviously, there is a correlation among different independent variables :The Nth X is equal to the (N - 1)th X multiplied by X.

May I ask whether this correlation will affect the value of the estimated value beta?

I would appreciate it if you could help me answer it.

thanks
Goulson

[rhondabacher]

Hi Goulson,

Thanks for your comment!

For the independent variables here (total counts for each cell), correlation might come into play if you have distinct groups of cells. In this case we recommend a group-specific normalization that is available in the package by specifying Conditions.

Let me know if any additional explanation would be helpful or if I misunderstood your question.

Best,
Rhonda

[GoulsonWang]

Thank you for your patient reply !

I'm afraid I haven't described the problem clearly enough.

When conducting the second quantile regression modeling in the article, the sequencing depth was taken as the independent variable, and the quantile of gene expression levels within the group was taken as the dependent variable.In the regression equation, since multiple genes within the same group are included, polynomials(multiple degrees d) are used to take into account more refined influences(That is, the multiple regression equation was established).At this point, the independent variables are sequencing depth and its functions . In sequence are the sequencing depth X, the square of the X, the cube of the X , the fourth power of X .....

What puzzles me is that in general, in regression equations, it is required that there should be no strong correlation among independent variables. However, here, it is obvious that each variable has a strong correlation (all independent variables are different powers of the sequencing depth X). Will this strong correlation among independent variables affect the estimation of the coefficient β1 in the multiple regression and thereby influence the estimation of the scaling factor SF.

Best,
Goulson