I am trying to determine if an equation is suitable to model Pressure drop vs fluid velocity. I have experimentally measured pressure drops for a variety of velocities, forming a curve, and I want to compare the measured values against what the equation outputs. What is the statistical method/approach that should be used to see if the equation is an appropriate model.
You can try the method of Linear Regression modeling/ Nonlinear Regression Modeling in this regard.
Well you might look at this link: https://www.bing.com/search?q=How+to+tell+if+a+curve+fit+works&pc=U528&form=QBLH&sp=-1&ghc=1&pq=how+to+tell+if+a+curve+fit+works&sc=2-32&qs=n&sk=&cvid=C41E4A18C89645F18F3087ECAECC360F
I would be tempted to look at a GAMS model knowing nothing about what you did.
A chemistry example is here: https://www.bing.com/search?q=michaelis+menten+fitting+by+generalized+additive+models&qs=n&form=QBRE&sp=-1&pq=michaelis+menten+fitting+by+generalized+additive+models&sc=1-55&sk=&cvid=6547667767F843D087B739DF71BDC162
Remember that the real question is how good is good enough. Polynomial interpolation can perfectly fit your data but predictions are usually awful. Good luck and Best wishes, David Booth
Indeed, the model-comparison approach provides several benefits: It strengthens the intuitive understanding of the material thereby increasing the ability to successfully analyze data in the future. It provides more control in the analysis of data so that readers can apply the techniques to a broader spectrum of questions. To do so, I would like to suggest you Article Information Technology Acceptance by Individual Professional...
https://s3.amazonaws.com/academia.edu.documents/4844123/pc2005.pdf?response-content-disposition=inline%3B%20filename%3DUnderstanding_the_relationship_between_c.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20200308%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20200308T044601Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=8bf058a3a3fb09a73369f7cd29d2e7f2c471e2363c86207da30249287fcd8bdb
https://books.google.com.au/books?hl=en&lr=&id=APusAgAAQBAJ&oi=fnd&pg=PP1&dq=data+analysis+model+comparison+approach&ots=BbTPxJ3h4Z&sig=a9uFOC9xQT_jbv7bLTl3_ZfCJUA#v=onepage&q=data%20analysis%20model%20comparison%20approach&f=false
So, I don't want to make a curve for the data, I want to compare using statistics how well the equation predicts the expected data. Sorry if my question was a bit ambiguous. I've read that I must use F and t-tests but I'm not sure how to apply them
Cameorn Jones ALWAYS look at a graph of your data. I think you are confused. Please consult a book like this one: https://www.bing.com/search?q=ewout+steyerberg+clinical+prediction+models&qs=RI&pq=steyerberg+ewout&sk=RI1&sc=2-16&cvid=B1FE727E5932407E9C7955A2642C55B0&FORM=QBRE&sp=2
Best Wishes, David Booth
Look at your data you can enter the data in SAS and that can help in curve fitting also help find the a suitable graph
You can also list your data in excel. Then plot a line graph. View the equation of the line first as linear grap (check its R-square value). Then choose a logarithmic one and check its R² value. Aim for higher R² and it directly tells you how much of the data predicts the graph/relation.
Given that you give no details of your experiment, there is a good chance you should have designed it differently. The key to answering your basic objective "to see if the equation is an appropriate model" is to get a good estimate of the measurement error, which you can then go on to use to see if the residuals from some fitted (or non-fitted theoretical) model are too large to be explained by measurement errors. To get a good estimate of the measurement error you would need to do something like a repeated-measurement experiment. You would then need to go on to see if the size of the measurement error is related to the experimental conditions. As others have suggested, plotting the data would be a good starting point.
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