# Python Curve Fitting Example

A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. curve_fit(). A particularly powerful feature of this package is that it takes, as input, a Python model function in symbolic form. Fitting in 1D. This is the Python version. Many built-in models for common lineshapes are included and ready to use. Plotting extrapolated data using curve fitting While plotting the CSV values, we have seen that there were some columns representing predictions of the world population in the coming years. Homework 2: A quick python code that filters, bins, and fits a line to data. What I basically wanted was to fit some theoretical distribution to my graph. Curve-Fitting¶ Here we are going to take a look at a few examples of fitting a function to data. There's no need on our part to put aside a validation set because learning_curve() will take care of that. approximate_curve() approximate_surface() Surface fitting generates control points grid defined in u and v parametric dimensions. This question led to a new package: hobby I found Metapost best for drawing complex smooth curves (i. This is useful in order to estimate any value that is not in the given range. Modeling Data and Curve Fitting. The following are code examples for showing how to use scipy. As with everything, there are choices to be made when producing a curve fit. Down load by right clicking and saving the file locally with the extension. OK, I Understand. Using the monthly swap market data, we fit the model to match exactly the one-year and ten-year points along the swap curve. On Nov 19, 2010, at 11:43 PM, cunninghands wrote: > need help curve fitting my data, I do not know how since I am very new to > Octave. The Trend function combines both steps in a single function, and returns exactly the same end result: = Trend(Y_1, X_1,. Being able to fit a model to experimental data is an extremely important laboratory skill. import numpy as np # Seed the random number generator for. This is because the higher polynomial produced a closer fit. Plotting extrapolated data using curve fitting While plotting the CSV values, we have seen that there were some columns representing predictions of the world population in the coming years. The paper is pulled through the marker by a falling weight. I'm using Python in a style that mimics Matlab -- although I could have used a pure object oriented style if I wanted, as the. The code then uses a genetic algorithm to train a neural network to approximate the same curve. This parameter is interpreted either as the number of evenly-sized (not necessary spaced) bins or the positions of the bin centers. To compute one standard deviation errors on the parameters use perr = np. The technique to determine K, the number of clusters, is called the elbow method. com Curve fitting examples in Excel, Libreoffice, Openoffice, python, R and others. Download Python source code: plot_curve_fit. Curve Fitting. Check out the scipy optimization tutorial for more examples. thank you for your help, but I need curve fit line sigmoid which called from gnuplot and also IC50 is written in the graph as sample i send. Numerical Methods Lecture 5 - Curve Fitting Techniques page 90 of 102 other examples of data sets that we can fit a function to. To compute one standard deviation errors on the parameters use perr = np. 7 supports 95% of top 360 python packages and almost 100% of top packages for data science. At first it is curve fit using a quadratic expression Z = a * x ^ 2 + b * x + c along a constant value of T i. SciPy offers module which provides algorithms for function minimization, root finding, curve fitting, etc. Clearly, such type of cases will include a polynomial term. So first we create a set of observation times: T = 500 dt = 10 nobs = int (T/dt + 1. Curve fitting definition is - the empirical determination of a curve or function that approximates a set of data. curve_fit, allowing you to turn a function that models your data into a Python class that helps you parametrize and fit data with that model. An example showing how to fit an HRF model to noisy peristimulus time-series data. In this post, I will show how to fit a curve with polynomial regression data and plot it in Python. Homework 1: A very basic python code example that reads a data file, plots the data, and overplots a model function. curve_fit(). Example showing the use of analytic derivatives in nonlinear least squares. Another often neglected aspect of using curve fits is enforcing the fit's range of applicability. In this post, I will show how to fit a curve with polynomial regression data and plot it in Python. Choose the Line function after selecting the Polynomial category. curve_fit is part of scipy. (4 replies) Friends, I wish to do some curve fitting with python by defining my own equations. In this example we fit a 1-d spectrum using curve_fit that we generate from a known model. There are several good tutorials on linear regression and curve fitting using python already available. A question I get asked a lot is 'How can I do nonlinear least squares curve fitting in X?' where X might be MATLAB, Mathematica or a whole host of alternatives. This extends the capabilities of scipy. This page deals with fitting in python, in the sense of least-squares fitting (but not limited to). Toggle Object Wire - Blender Addon. To compute one standard deviation errors on the parameters use perr = np. In python I have a function which has many parameters. A common use of least-squares minimization is curve fitting, where one has a parametrized model function meant to explain some phenomena and wants to adjust the numerical values for the model so that it most closely matches some data. Your plots should match the provided sample outputs. Notice that the curve is fit closer, shown by the smaller residuals and lower value for the sum-of-squares of the residuals. dll) or via the external bindings to Gpufit (e. Many of the script examples below are applicable also when creating custom tools and other extensions as embedded IronPython scripts or converted to C#. First we de ne a function, then use it in the formula for nls. There's no need on our part to put aside a validation set because learning_curve() will take care of that. cstride for default sampling method for wireframe plotting. Polynomial regression is a nonlinear relationship between independent x and dependent y variables. The author has carefully developed a concise approach to using Python in any discipline of science and engineering, with plenty of examples, practical hints, and insider tips. I am confident my experiences in both the Cornell Hedge Fund and my business fraternity, Phi. Speeding up the training. Jakub Prchlik's python tutorials from my Spring 2015 ASTR 222 course. curve_fit, allowing you to turn a function that models for your data into a python class that helps you parametrize and fit data with that model. For the Cavendish experiment, we'll need to fit our data to a sinusoidal curve with exponential decay. I would like to adapt your code for my data. A normal Gaussian. Curve fitting is used in a wide spectrum in engineering applications such as cars and air crafts surface design. I’m a big Python guy. Bake Helper - Blender Addon. Curve fitting examples in Excel, Libreoffice, Openoffice, python, R and others. In general, any callable object can be treated as a function for the purposes of this module. Each code example is demonstrated on a simple contrived dataset that may or may not be appropriate for the method. Fitting exponential decay in Python3. Peak Fitting in Python/v3 Learn how to fit to peaks in Python Note: this page is part of the documentation for version 3 of Plotly. Curve fitting¶ Demos a simple curve fitting. leastsq that overcomes its poor usability. Python can do these things, but the modules are scattered (there’s at least three separate modules to fit curves that people have written to do different things) and don’t always give the needed output. Where A is the amplitude of the curve, c is the offset from zero and k is the rate constant. 1D Examples and Exercise¶. Here's the output of the python script, where blue is the data, orange is the negative exponential, and green is the 9th order polynomial fit: As can be seen in the image, the 9th order polynomial fit is really good for the first part, but deviates massively past 100000 feet. One choice is whether to include a trendline or to perform a true curve fit. SOLUTION:-Basically, Curve Fitting is the process of constructing a curve or mathematical functions which possess the closest proximity to the real series of data. Natural Language Processing. If you have replicate Y values at each X value, format the table for entry of replicates. We’ll start with straight lines, then expand the concept. Algorithm for multi-curve-fitting with shared parameters and a possible application in evoked compound action potential measurements Philipp Spitzer , 1 Clemens Zierhofer , 2 and Erwin Hochmair 1 1 University of Innsbruck, Institute of Applied Physics, Technikerstrasse 25, 6020 Innsbruck, Austria. Download Python source code: plot_curve_fitting. It is considered bad, because this time for example you had same bug repeated 14 times in your code, for example. array([1, 4, 1, 3]) def fit_func(x, a, b): return a*x + b params = curve_fit(fit_func, x, y) [a, b] = params This code will return a = 0. But we're not stuck with just straight line fits. You can specify variables in a MATLAB table using tablename. Scipy: curve fitting. Solution 8. The content of this site is licensed under the Creative Commons Attribution-NonCommercial 4. Fitting a spectrum with Blackbody curves¶. Elements of Python programming. Examine the solution process to see which is more efficient in this case. I have a set of data and I want to compare which line describes it best (polynomials of different orders, exponential or logarithmic). You can test the accuracy of the model later. rcParams. Univariate interpolation is basically an area of curve-fitting which finds the curve that provides an exact fit to a series of two-dimensional data points. Here's a plot with your points and the linear fit which is clearly a bad one, but you can change the fitting function to obtain whatever type of fit you would like. The main problem is, given a set of points in the plan, we want to fit them in a smooth curve that passes through these points. Open the Curve Fitting app by entering cftool. Like this one, for example:. Overview of Curve Fitting. fit a sigmoid curve, python, scipy. Global Fitting, also called Global Analysis, allows you to fit multiple data sets in a single curve fit. Polynomial curve fitting. Import the data "\Samples\Curve Fitting\Linear Fit. Exponential Linear Regression | Real Statistics Using Excel Non-linear fitting with python in 1D, 2D, and beyond Read more. predict(X): Predict the class value for X score(): Returns the mean accuracy for the model In Pandas: Python Data Analysis Library: In Orange:. , from an oscilloscope). Change the model type from Polynomial to Gaussian. Make sure your current project uses Python as its interpreter by selecting the menu point Scripting->Scripting Language and double-clicking on "Python" in the resulting dialog (if the dialog appears, but does not contain the "Python" item, your installation of SciDAVis has been compiled without Python support). Curve fitting and surface fitting web application source code Django (this site) Django (Python 2) Flask CherryPy Bottle Curve fitting and surface fitting GUI application source code tkinter pyQt5 pyGtk wxPython Miscellaneous application source code Animated Confidence Intervals Initial Fitting Parameters Multiple Statistical Distributions Fitter. use('TkAgg') #or maybe qt4agg, or gtkagg from pylab import * print "Example of switching between log and linear axes Won't work correctly on Windows using IDLE. Let's start off with this SciPy Tutorial with an example. To the firm, I will bring my strong ability to work in a team, enthusiasm, and ability to balance multiple priorities. This is because the higher polynomial produced a closer fit. The source code generated by XYmath will print warnings if the curve fit is called with an x value outside of the x data range. Improved curve-fitting with the Model class. Linear curve fitting (linear regression). In this post, I will show how to fit a curve with polynomial regression data and plot it in Python. This example is only applicable for large data compared to the number of all weights of input and hidden nodes. The example shows how to determine the best-fit plane/surface (1st or higher order polynomial) over a set of three-dimensional points. I would like to adapt your code for my data. Univariate interpolation is basically an area of curve-fitting which finds the curve that provides an exact fit to a series of two-dimensional data points. Jakub Prchlik's python tutorials from my Spring 2015 ASTR 222 course. Curve Fitting. Python's curve_fit calculates the best-fit parameters for a function with a single independent variable, but is there a way, using curve_fit or something else, to fit for a function with multiple independent variables? For example: def func (x, y, a, b, c): return log (a) + b * log (x) + c * log (y). The objective of a Linear SVC (Support Vector Classifier) is to fit to the data you provide, returning a "best fit" hyperplane that divides, or categorizes, your data. Here is an example Python code description. The main idea is that we know (or…. 0 500 1000 1500 2000 2500 3000 3500 4000. To compute one standard deviation errors on the parameters use perr = np. Two quantities are independent if one has no effect on the other. Modeling Data and Curve Fitting. ought about using the curve_fit function from scipy. What I basically wanted was to fit some theoretical distribution to my graph. First, importing the necessary pieces: import numpy as N import pylab as P from mvpa. Curve Fitting¶ One of the most important tasks in any experimental science is modeling data and determining how well some theoretical function describes experimental data. Algorithm Background There are two different categories of CPD–offline and online. Keras Tutorial: The Ultimate Beginner’s Guide to Deep Learning in Python Share Google Linkedin Tweet In this step-by-step Keras tutorial, you’ll learn how to build a convolutional neural network in Python!. Consequently, Python has found ample application in academic curricula. The diagonals provide the variance of the parameter estimate. Since he was learning to program computers, he started writing curve fitting software, first in C and then in C++. I'm trying to find good alternatives to the standard curve_fit() in SciPy because I'm working on a grid-computing system that has a slightly dated version of Python (2. To implement least-squares curve fitting, your objective function will need to find the residual at each data point, square the values, and sum them up. Here is an ex…. If we try to fit a linear model to curved data, a scatter plot of residuals (Y axis) on the predictor (X axis) will have patches of. Fit Using differential_evolution Algorithm¶. ) or 0 (no, failure, etc. One method of curve fitting is linear regression -it minimizes the "square of the errors" (where the "error" is the distance each point is from the line). I found a couple other curve fitting libraries (some are wrappers to C/Fortran libs I don't have), and I found a. Your plots should match the provided sample outputs. Curve Fitting Curve fitting is a process of determining a possible curve for a given set of values. A proprietary programming language developed by MathWorks, MATLAB allows matrix manipulations, plotting of function and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C , C++. This is a an example of a Python program that asks for a value, calculates a result, and displays it for the user. py The Levenberg-Marquardt algorithm is frequently used in mathematics and computing to solve non-linear problems. Packages ›› Example Python 3 Django site for curve fitting and surface fitting A Django site in Python 3 for curve fitting 2D and 3D data that can output source code in several computing languages and run a genetic algorithm for initial parameter estimation. Least squares problems arise in the context of ﬁtting a. 3,15) #we will make y the response variable and x the predictor #the response variable is usually on the y-axis plot(x,y,pch=19) Looks like we can fit a nice curve there. plot import plotErrLine from mvpa. We don't even need consider the above equation unless we want to get under the hood and mess around or do other forms of customization. More details. Iterative curve fitting also takes longer than linear regression - with typical modern personal computers, an iterative fit might take fractions of a second where a regression would take fractions of a millisecond. Q&A for finance professionals and academics. Takes a text file as input that contains the x and y coordinates of a series of points on a curve. Data in this region are given a lower weight in the weighted fit and so the parameters are closer to their true values and the fit better. cstride for default sampling method for wireframe plotting. pylab_examples example code: #!/usr/bin/env python import numpy as np import matplotlib. Regularized regression : Importance of regularization cannot be overstated as it is a central concept in machine learning. How to choose between using IronPython scripting and creating a C# Extension when developing for TIBCO Spotfire® How to develop IronPython scripts and their limitations. Example: x. A 2-d sigma should contain the covariance matrix of errors in ydata. cvfit = cvglmnet(x, y) – fits the model by cross-validation under all default settings, with results saved in cvfit. Change the model type from Polynomial to Gaussian. So for example's. LAB Fit fits functions of one and several independent variables (from 1 up to 6), admitting uncertainties at the dependent variable (Y) and also at the independent variables (X). By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy. Fitting a support vector machine¶ Let's see the result of an actual fit to this data: we will use Scikit-Learn's support vector classifier to train an SVM model on this data. it is very sensitive to varying. Plotting is provided through the Chaco 2D plotting library , and, optionally, Mayavi for 3D plotting. Curve Fitting in Python not fitting my curve. This page deals with fitting in python, in the sense of least-squares fitting (but not limited to). For example, it is inherently non-local, i. Example: Approximate Curve Fitting. We then fit the data to the same model function. The diagonals provide the variance of the parameter estimate. So first we create a set of observation times: T = 500 dt = 10 nobs = int (T/dt + 1. It is considered bad, because this time for example you had same bug repeated 14 times in your code, for example. Here's an example for a linear fit with the data you provided. This is a Python tutorial but some statistics are inevitable! How to use implemented routines: leastsq, curve_fit and Simplex. I want to fit this function to a data set, but using only one parameter, the rest of the parameters I want to supply on on my own. Since he was learning to program computers, he started writing curve fitting software, first in C and then in C++. Like this one, for example:. differential_evolution() method carries out a standard least-squares non-linear fit (using scipy. Both Numpy and Scipy provide black box methods to fit one-dimensional data using linear least squares, in the first case, and non-linear least squares, in the latter. A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. During the research work that I’m a part of, I found the topic of polynomial regressions to be a bit more difficult to work with on Python. gnuplot supports these nonlinear curve fits, and can even take the experimental uncertainties of the data points into account. com Curve fitting examples in Excel, Libreoffice, Openoffice, python, R and others. This group of models finds a relationship between input and output variables by using the methods. Both data and model are known, but we'd like to find the model parameters that make the model fit best or good enough to the data according to some metric. There, we discussed UV-decomposition of a matrix and gave a simple algorithm for ﬁnding this decomposition. Plots, Curve-Fitting, and Data Modeling in Microsoft Excel This handout offers some tips on making nice plots of data collected in your lab experiments, as well as instruction on how to use the built-in curve-fitting routines in Microsoft Excel. Fitting in 1D. We can then use this to improve our regression, by solving the weighted least squares problem rather than ordinary least squares (Figure 5). com Curve fitting examples in Excel, Libreoffice, Openoffice, python, R and others. For example: \$\ c_0 + c_1 \cdot cos (b_0 + b_1\cdot x + b_2\cdot x^2+ b_3\c Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. I have a set of data and I want to compare which line describes it best (polynomials of different orders, exponential or logarithmic). You can specify variables in a MATLAB table using tablename. , the dependent variable) of a fictitious economy by using 2 independent/input variables:. Most physics students are familiar with linear curve fitting, often with a spreadsheet or data-collection software such as _Data Studio_ (PASCO Scientific) or _Logger Pro_ (Vernier Software). So Python is actually a great fit for a bunch of startups--it's the modern lowest common denominator. Here is an example of a less extreme curve linear association between urban rate, and female employment rate, with a linear regression line. The multidimensional nature of such regressions makes them more difficult to visualize, but we can see one of these fits in action by building some example data, using NumPy's matrix multiplication operator:. 0 International License. Related course: Python Machine Learning Course; Determine optimal k. Python) submitted 2 years ago by Eigenspace Hey there, I own an iPad Pro and I love its portability and I find I actually like its onscreen keyboard so I've been thinking that I want to start using it a my main machine for data analysis in my lab since I've been having a great time using python in the. Logistic Regression Assumptions. In the same way seaborn builds on matplotlib by creating a high-level interface to common statistical graphics, we can expand on the curve fitting process by building a simple, high-level interface for defining and visualizing these sorts of optimization problems. According to the Figure on pages 34-35 of this study, which of these are the top six Scarce but Valuable Computer Skills for STEM Employers? (measured by duration of job posting and highest salaries). For other relationships we can try fitting a curve. R offers to statements: qqnorm(), to test the goodness of fit of a gaussian distribution, or qqplot() for any kind of distribution. glmnetPlot(fit) – plots the coefficients from the fitted object. It seems that the data points fit to a logistic like curve only a little shifted and stressed. MAP, which computes maximum a posteriori estimates. He left Tokyo, Japan in early 2000, returning to Birmingham, Alabama, and started programming in Python. In this case, the optimized function is chisq = sum((r / sigma) ** 2). The available models are those registered by the pymodelmit. Find the periods in the light curves. Algorithm Background There are two different categories of CPD–offline and online. py rather than. The document for tting points with a torus is new to the website (as of August 2018). We’ll start with straight lines, then expand the concept. You can test the accuracy of the model later. approximate_curve() approximate_surface() Surface fitting generates control points grid defined in u and v parametric dimensions. Task 7 : Fit a power model and intercept. make the model extremely. 2 Objectives 1. According to the Figure on pages 34-35 of this study, which of these are the top six Scarce but Valuable Computer Skills for STEM Employers? (measured by duration of job posting and highest salaries). The algorithms are translated from MINPACK-1, which is a rugged minimization routine found on Netlib, and distributed with permission. Curve fitting¶ A curve fitting example. See the following reasons to support Python 3. Like leastsq, curve_fit internally uses a Levenburg-Marquardt gradient method (greedy algorithm) to minimise the objective function. Matlab has a curve fitting toolbox (installed on machines in Hicks, but perhaps not elsewhere on campus - as of Sept. Getting started with Python for science Demos a simple curve fitting. Curve-Fitting¶ Here we are going to take a look at a few examples of fitting a function to data. >>> Python Software Foundation. Moreover, early stopping can be used based on the internal validation step. I have the best fitting curve at the end of my code. This extends the capabilities of optimize. Curve Ensemble is a free C++ open-source project for fitting, editing, and painting curves. Here is an ex…. 5,158) y <- c(99. This work is licensed under a Creative Commons Attribution-NonCommercial 2. Assayfit Pro is a curve fitting API for laboratory assays and other scientific data. This npm module is a node wrapper for which you can use JavaScript to access the power of the optimize module. Fit Using differential_evolution Algorithm¶. As shown in the previous chapter, a simple fit can be performed with the minimize() function. Cannot contain Inf or NaN. Note: this page is part of the documentation for version 3 of Plotly. Curve Fitting with Matlab. Fitting a spectrum with Blackbody curves¶. It seems that the data points fit to a logistic like curve only a little shifted and stressed. Fitting such type of regression is essential when we analyze a fluctuated data with some bends. Curve Fitting Curve fitting is a process of determining a possible curve for a given set of values. The final coefficients are physically meaningless and also of no interest. Data in this region are given a lower weight in the weighted fit and so the parameters are closer to their true values and the fit better. See the following reasons to support Python 3. import numpy as np. Fitting a support vector machine¶ Let's see the result of an actual fit to this data: we will use Scikit-Learn's support vector classifier to train an SVM model on this data. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. Hey, here is the GitHub link for python implementation for the Levenberg-Marquardt algorithm for curve fitting. The interesting matter here is the architecture you choose. Curve fitting definition is - the empirical determination of a curve or function that approximates a set of data. The following are code examples for showing how to use scipy. Curve Fitting. 7 if you learn it today. py, which is not the most recent version. A 1-d sigma should contain values of standard deviations of errors in ydata. Could someone please give some guidance or examples on doing the same. How to fit a model with nonlinear regression. You can specify variables in a MATLAB table using tablename. It is important to make sure that the data you have obtained can be represented in a way that is repeatable. Create and manipulate arrays (vectors and matrices) by using NumPy. Fitting such type of regression is essential when we analyze a fluctuated data with some bends. Polynomial Curve Fitting. Matlab has two functions, polyfit and polyval, which can quickly and easily fit a set of data points with a polynomial. The curve is a horizontal, straight line represented by the general form equation… y = k. , approaches an asymptote), you can fit this type of curve in linear regression by including the reciprocal (1/X) of one more predictor variables in the model. Instead insert print functions and any input statement for pause or use debugger break points and watches. Data format description. We will use a SVM classifier for this example. The plot shows the function that we want to approximate, which is a part of the cosine function. In this post, I will show how to fit a curve with polynomial regression data and plot it in Python. An example showing how to fit an HRF model to noisy peristimulus time-series data. Consequently, Python has found ample application in academic curricula. Compare the results of fitting with the default 'trust-region-reflective' algorithm and the 'levenberg-marquardt' algorithm. you cannot have two separate Y's for the same X. A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. Here are some examples of the curve fitting that can be accomplished with this procedure. MATLAB has two functions, polyfit and polyval, which can quickly and easily fit a polynimial to a set of data points. python-examples / examples / scipy / fitting a gaussian with scipy curve_fit. Then how can one find the best fitting curve? I believe there will be some data for which we can not find any regular pattern. I’m looking for an ArcGIS tool or script that will delete all the collinear vertices in line features. For example: \$\ c_0 + c_1 \cdot cos (b_0 + b_1\cdot x + b_2\cdot x^2+ b_3\c Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Curve Fitting in Matlab. In other words, size_u and size_v arguments are used to fit curves of the surface on the corresponding parametric dimension. To compute one standard deviation errors on the parameters use perr = np. 7 is year 2020. Your input may be faces and labels may be names but, just as well, your input may be numbers (or vectors or what whatever the input generating your curve is) and your outputs are the curve values. pyplot import * import scipy from scipy. Curve Fitting Least Square Method Example. Task 7 : Fit a power model and intercept. curve_fit (parabola, x, y_with_errors) It returns two results, the parameters that resulted from the fit as well as the covariance matrix which may be used to compute some form of quality scale for the fit. My function is (where Ti is initial hot. Fitting in 1D. Exponential Fit in Python/v3 Create a exponential fit / regression in Python and add a line of best fit to your chart. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to$585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over$1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: