Art of Stat: Concepts vs Least Squares Curve Fit Kullanım & İstatistikleri

Explore the Central Limit Theorem, learn about the correlation coefficient and linear regression, and visualize the coverage probability of confidence intervals or Type I & II Errors in hypothesis testing. Build understanding by experiencing these important concepts step-by-step. For students and teachers of statistics. The Art of Stat: Concepts app provides access to the following modules: - Central Limit Theorem for Means - Central Limit Theorem for Proportions - Explore Correlation - Explore Linear Regression - Explore Coverage - Errors & Power CLT: Select from several real population distributions (left and right-skewed or fairly symmetric) and simulate taking a sample from the population. Visualize how the sampling distribution builds, step-by-step. Explore the effect on the sampling distribution as you increase the sample size. Overlay the normal distribution. Compare the sampling distribution of the mean to the population distribution, both visually and in terms of key statistics. Explore Correlation/Linear Regression: Create (and delete) points in a scatterplot by tabbing on the screen. Show the regression line or residuals. Simulate scatterplots and guess the correlation coefficient. Coverage and Errors: Explore what 95% coverage for a confidence interval for a population mean or proportion implies. See the Type I and Type II error and explore how they depend on the sample size and the true parameter value. Find and visualize the power of a hypothesis test.
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“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app. User inputs point sets and chooses function types. Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs. Point sets can be stored in a table and are available after app is closed. Currently available function types are: 2D: 1. Line. 2. Parabola. 3. Polynomial up to 8th degree. 4. Circle. 5. Conic section (Ellipse or Hyperbola). 6. Trigonometric function as C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x), where user can select n between 1 and 8 and enter any ω. 7. Exponential Function. 8. Bell Curve. 3D: 1. Plane. 2. Sphere. Also, there is an option to choose the Best Fit: the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals. In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD. Links to four other free apps by same developers are included in the app: 1. “Matrix Solver Step by Step” Linear Algebra Visual Guide. 2. “Polynomials and Linear Systems” Equation Solver. 3. “GraphMath” Graphing Calculator. 4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide. Developers hope to get feedback from users at graphmath@aol.com.
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Art of Stat: Concepts VS.
Least Squares Curve Fit

Aralık 10, 2024