Determining functional relation of two dependant variables

Click For Summary
SUMMARY

The discussion centers on determining the functional relationship between two dependent variables: temperature and conductivity over time. The user, Fritz, seeks methods to analyze these correlated datasets, particularly when both variables are influenced by time. While traditional regression techniques are effective for independent variables, the conversation suggests using loess smoothing combined with cubic splines as a viable approach for this scenario. The need for literature or MATLAB/Octave routines to support this analysis is also highlighted.

PREREQUISITES
  • Understanding of regression analysis techniques
  • Familiarity with loess smoothing methods
  • Knowledge of cubic spline interpolation
  • Basic proficiency in MATLAB or Octave programming
NEXT STEPS
  • Research loess smoothing techniques for data analysis
  • Explore cubic spline interpolation methods
  • Learn how to implement regression analysis in MATLAB
  • Investigate literature on analyzing correlated datasets with time as a parameter
USEFUL FOR

Researchers, data analysts, and scientists working with time-dependent datasets, particularly those analyzing the relationship between temperature and conductivity in laboratory settings.

fsonnichsen
Messages
61
Reaction score
5
I have a pair of correlated datasets that I collected in the lab for temperature and conductivity of a solution vs time. I want to determine the functional relation between the two. (see attached plot-an interesting lead/lag in the phase difference).
If I were trying to determine this relation using for example a carefully controlled temperature I would just use a regression against some order of polynomial on the temperature (the relation is almost linear). However in the present case the temperature varies in an undetermined fashion.
There is a lot of literature out there for doing this when one variable is independent but I cannot find something for both variables dependent on some other parameter (time here). What is the method for doing this and perhaps some texts describing this (or matlab/octave routines for that matter)
Thanks
Fritz
 

Attachments

Last edited:
Physics news on Phys.org
I have seen plenty of analyses that estimate relations between variables from observations where both variables were random. I am not aware of any reason for wanting one of the variables to be controlled, other than that where that is the case one can choose values for that variable in such a way as to eliminate sparsely-covered regions in the range of interest. Is there any reason not to just use a technique such as loess together with cubic spline?
 

Similar threads

Undergrad Variable Normalization for different variable ranges....
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Linear regression and random variables
  • · Replies 30 ·
2
Replies
30
Views
5K
Undergrad Parameters of a distribution of a physical variable
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Random variable vs Random Process
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Linear Model with independent categorical variable
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Multicollinearity and Interactions
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Expected coefficient change from simple to multiple linear regression
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Principal Component Analysis with dependent variable?
  • · Replies 3 ·
Replies
3
Views
3K
High School Choosing which variable is the dependent or independent variable
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad How to propagate errors through a regression & non-linear model?
  • · Replies 8 ·
Replies
8
Views
3K