Excel curve fit

Different about 3 and 4 terms' check bsista comment on this post. I am not sure if you have to use creep options, but if yes then check this from Peter.Firstly, Fig 3 represents also the values in between and therefore 7 Prony parameters. bsista said that we can use 1s, 1e3s and 1e7s to have only 3 prony shear parameters and still have a good distribution of time (and therefore a better curve fit).I hope it helps a bit. Sangrey Subscriber --> jonsys,Thank you for the reply, your explanation is very helpful to me. (i) I don't use Isotropic Elasticity to define Young's Modulus(E), Poisson's Ratio(v), Bulk Modulus and Shear Modulus, specifically G, but still find G-inf [Fig.1]. Have you tried yet?(ii) The line in Curve-fit [Fig.2] is different from the line in Prony Shear Relaxation (almost straight line) [Fig.3]. Is that a problem? Fig.1 Fig.2 Fig.3Thanks for your help, thanks for your time. jonsys Subscriber --> Hello Sangrey,I am not sure I understood correst your first questions; but I haven't tried to define G inf (if that's what you asked)2. There is a problem in visualization if you are using other version of ANSYS rather than v19.0 (.1 or .2)If the time is big in your case, right click on the x-axis of the graph and make it logarithmic scale - it is easier to judge the curve fitting.One way to check curve fit is to build yourself in excel (or whatever) the curve using prony coefficient generated

C(t) is the concentration of the CA in the voxel of interest at time t, v is the volume fraction of the indicator distribution space and Ca(t) is the concentration of the CA in the arterial compartment at time t. Here, v can represent the plasma volume fraction (vp) in a voxel that is highly vascularized with no vascular/extravascular exchange, the extravascular volume fraction (ve) in a weakly vascularized voxel, or v = vp + ve in a fast-exchange scenario. A statistical F-test is used to evaluate the likelihood that an observed improvement of fit to the data, using a model with higher number of parameters, warrants the use of additional parameters [42]. A p-value In the current implementation, the Patlak model represents the two-parameter form of the two-compartment model with the extended Tofts model with three parameters being at the top of the nested hierarchy [23, 24, 37].Options to smooth the dynamic signal time course and to fit specific ROIs versus voxel-by-voxel fitting are also available in the DCE-MRI sub-module (Fig. 2c). 4) While models belonging to the same hierarchy can be folded into the nested model fitting option, it may be desirable to compare non-nested models or make comparisons with different statistical tests. The fitting analysis sub-module allows for visual and statistical assessment of goodness-of-fit (Fig. 2d). Model fits with 95 % prediction bounds of the fit are shown graphically along with the raw data for each voxel/ROI. Fits between models can be compared using the F-test [42, 43], fraction of modeled information (FMI) and fraction of residual information (FRI) [35], and the Akaike information criterion [7, 43]. These results can be exported to an Excel (office.microsoft.com/en-us/excel) spreadsheet for offline analysis. Estimation of model parametersAll curve fitting functions in ROCKETSHIP are implemented using MATLAB’s Curve Fitting Toolbox. T1, T2 and ADC signal equations can be linearized and fitted with linear regression (See Appendix A). Alternatively, these parameters can be directly fitted with non-linear methods. ROCKETSHIP uses the trust region algorithm provided in the Curve Fitting Toolbox to perform non-linear least squares regression. For T1, T2 and ADC regression, the parameters are hard-coded to have non-negative value constraints. Robust curve fitting is dependent on appropriate starting parameters for the fitting routine [44]. To facilitate this process, a preferences text file defining parameter constraints and convergence criteria, such as fitting tolerances and maximum numerical of iterations, is provided to allow easy editing of these variables. This text file is read by ROCKETSHIP when AIF and model fitting sub-modules are run.During testing of ROCKETSHIP, it was found that Ktrans fitting often converged to local minima instead of the desired global minimum solution. To address this, Ktrans was fitted using multiple starting values with the fit value converging with the lowest residual used as the final value. Other variables were less sensitive to the starting position and thus a single initial value was used to fit each of those variables.Voxel-wide fitting is performed in parallel using functions provided by MATLAB’s Parallel Computing

Timesaver.Once your data is in place, take a moment to plot it. Highlight your data, go to the "Insert" tab, and select a scatter plot. This visual check can help you see if nonlinear regression is indeed necessary. If your data points form a curve, then you're on the right track.Remember, the key to effective analysis is good data organization. A clear and tidy spreadsheet will make the regression process much more manageable.Excel might not be the first tool you think of for nonlinear regression, but it has some built-in features that can get the job done. While it's not as robust as specialized statistical software, Excel's capabilities are sufficient for many applications.To perform nonlinear regression in Excel, you can use the "Solver" add-in. Solver is a powerful tool that can handle various optimization problems, including finding the best-fit parameters for nonlinear models.To activate Solver, go to "File" > "Options" > "Add-ins." Under "Manage," select "Excel Add-ins" and click "Go." Check the box next to "Solver Add-in" and click "OK." You should now see Solver in the "Data" tab.Once Solver is active, you can set up your regression model. Suppose you’re modeling a dataset with an exponential growth pattern. You'll need to define your model equation, such as y = a * e^(b * x), where a and b are parameters to be estimated.Enter a guess for these parameters in your spreadsheet. Then, use a formula to calculate the predicted y values based on your model and parameter guesses. Finally, define an objective function, such as minimizing the sum of squared differences between your observed and predicted values.With everything set up, open Solver. Set your objective function cell, choose "Min" to minimize it, and define your parameter cells as variables to change. Click "Solve," and Solver will iterate to find the best-fit parameters. It’s a bit like magic, only with more spreadsheets involved.Polynomial regression is a type of nonlinear regression where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial. Excel makes it relatively straightforward to perform polynomial regression using the trendline feature in charts.First, ensure your data is plotted in a scatter plot. Once your data is visualized, you can add a trendline. Click on any data point in your scatter plot, and you'll see an "Add Trendline" option appear. Select it, and Excel will offer various types of trendlines, including polynomial.Choose the polynomial option and decide on the degree of the polynomial. Typically, a second or third-degree polynomial is a good starting point, but this depends on the curve of your data. Excel will then fit a polynomial line to your data points.Interestingly enough, Excel also allows you to display the equation of the polynomial on the chart. This equation can be handy if you need to predict future values or further analyze the relationship between your variables.Keep in mind that while polynomial regression can model complex data patterns, it can also lead to overfitting if the degree

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Before diving into Excel specifics, let’s clarify what nonlinear regression is. In a nutshell, nonlinear regression is a form of regression analysis where observational data is modeled by a function that is a nonlinear combination of model parameters and depends on one or more independent variables.Unlike linear regression, where the relationship between variables is a straight line, nonlinear regression fits data to a curve. This is particularly useful when your data doesn’t fit a straight line and instead follows a more complex pattern. Examples include exponential growth, logistic growth, and polynomial trends.To grasp this concept, imagine you're plotting the growth of a plant over time. Initially, the growth might be slow, then accelerate rapidly, and finally taper off as it reaches maturity. A simple linear regression wouldn't capture these subtleties, but nonlinear regression can.In practical terms, nonlinear regression is invaluable in fields like biology, economics, and engineering, where data often exhibits nonlinear relationships. So, understanding how to perform nonlinear regression in Excel can help you make sense of complex data in these and other areas.Now that we know what nonlinear regression is, the next question is: when should we use it? Nonlinear regression is ideal when your data displays a curve, as opposed to a straight line. But how do you determine this?One way to tell is by plotting your data. If you notice that the points form a distinct curve rather than a line, nonlinear regression could be the way to go. This is particularly true in scenarios involving exponential growth, such as population studies or chemical reactions, where the rate of change increases rapidly over time.Another common scenario is logistic growth, often seen in populations with a carrying capacity. Here, growth starts off exponential but slows as it approaches a maximum limit. Again, a simple line wouldn't do justice to this pattern. Polynomial trends, with their characteristic U or S shapes, are also candidates for nonlinear regression.In Excel, nonlinear regression is useful when you need to model these complex relationships without the need for specialized software. It's a handy skill for anyone dealing with data analysis, from business analysts to academic researchers. So, if you find your data isn't fitting a straight line, it's time to consider nonlinear regression.Alright, let's get practical. Before running any analysis, you need to set up your data in Excel properly. This setup is crucial because a well-organized spreadsheet makes the whole process smoother and more intuitive.Start by opening a new Excel workbook. Enter your independent variable data in one column and your dependent variable data in the adjacent column. Label these columns clearly at the top, for example, “Time” and “Growth.” This step is pretty straightforward, but it's surprising how much easier it makes things later on.If you have a lot of data, consider using Excel's table feature. Highlight your data, click on the "Insert" tab, and select "Table." This not only makes your data look nice but also allows you to use table references in formulas, which can be a real