Finding the Best fitting curve for a graph?

In summary, the speaker conducted an experiment on the effect of different salinities on the absorption of Polyacrylic acid. The results showed a difference in absorption between trials and varying salinity levels. The original mass of the polymer was 3g. The speaker is seeking assistance in finding the best fitting curve for the graph with more data points needed to accurately represent the relationship between salinity and absorption.
  • #1
Ascleipus
21
0
Hi, I m unsure whether or not this should perhaps be in the homework forum, however one might say this is more of a technical issue. I recently conducted an experiment for a report I intend to write up promptly, and I wanted to find the best fitting curve for these values. I tested how different salinities affect the degree of absorption of Polyacrylic acid. This is what I found
Trial 1 Trial 2
Salinity 0M 558g 533g
0.25M 95g 93g
0.5M 79g 79g
0.75M 63g 67g
1M 54g 60g

original mass of the polymer was 3g.

Essentially what I would love to find out is how I might be able to get a best fit curve for this graph.

Help would be much appreciated:smile:
 
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  • #2
I don't see how to do it without knowing a priori what kind of function described the dependence. Apparently at low salinities the result is extremely dependent on the concentration, so you would need much more data points to cover this area to be able to suggest something that would be not just a wild guess.
 

What is the purpose of finding the best fitting curve for a graph?

The purpose of finding the best fitting curve for a graph is to accurately represent the relationship between two variables and make predictions based on the data. This is important in scientific research and data analysis to draw meaningful conclusions and make informed decisions.

What is the difference between linear and non-linear curves?

A linear curve is a straight line that represents a linear relationship between two variables, where the change in one variable is directly proportional to the change in the other. A non-linear curve, on the other hand, is a curved line that represents a non-linear relationship between two variables, where the change in one variable is not directly proportional to the change in the other.

What are the common methods used to find the best fitting curve for a graph?

The common methods used to find the best fitting curve for a graph include the method of least squares, regression analysis, and visual inspection. The method of least squares involves minimizing the sum of the squared differences between the data points and the curve. Regression analysis involves fitting a mathematical equation to the data points. Visual inspection involves visually comparing different curves to the data points to determine the best fit.

What are the limitations of finding the best fitting curve for a graph?

One limitation is that the best fitting curve may not accurately represent the actual relationship between the variables, especially if the data is noisy or if there are outliers. Another limitation is that the best fitting curve may not be able to predict future data points with 100% accuracy, as it is based on existing data and may not account for unforeseen variables.

How can one determine if a curve is the best fit for a graph?

One way to determine if a curve is the best fit for a graph is by calculating the coefficient of determination (R-squared). This value ranges from 0 to 1, with 1 indicating a perfect fit. Another way is to visually compare the curve to the data points and see if it accurately represents the trend and pattern of the data. Additionally, conducting a significance test can determine if the relationship between the variables is statistically significant.

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