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Fit tool Fit is one of the GraphSight tools used to perform regression analysis using different regression models based on the least squares method. It also makes it possible to add the calculated smoothing curve to the plot and displays common statistical information for the data of a table-defined graph. A little theory first. Regression Model is a a statistical procedure called regression analysis, the model predicts or projects what things would have been like had there been no intervention. Least Squares Fitting is a mathematical procedure for finding the best fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve. GraphSight makes use of this method while finding a fitting curve. Regression is a method for fitting a curve (not necessarily a straight line) through a set of points using some goodness-of-fit criterion. GraphSight makes it possible to process with the reciprocal, gauss, hyperbolic, linear, logarithmic and polynomial regression models. To apply the fit tool to the Table defined graph select it with the mouse and go to the Graphics|Tools|Fit... programs main menu option. You will be presented with the Fit tool dialog. Step 1 The first step of GraphSight Fit tool wizard lets you select a particular regression model to deal with. The generalized formula of the resulting curve appears on the right while you are making you selection.
Reciprocal calculates the best fitting reciprocal line curve for a given set of data. The curve is determined by the equation
The values of x and y are taken from the table graph, the parameters k0, and k1 are estimated using a least squares approximation. A minimum number of 2 values is required in order to apply this regression model. Gauss calculates the best fitting Gaussian curve (normal distribution) for a given set of data. The curve is determined by the equation
The values of x and y are taken from the table graph, the parameters k0, k1, and k2 are estimated using a least squares approximation. Hyperbolic calculates the best fitting Hyperbola for a given set of data. The Hyperbola is determined by the equation
The values of x and y are taken from the table graph, the parameters k0, and k1 are estimated using a least squares approximation. Linear estimates the best fit of a straight line to a sample of two-dimensional data points using linear regression. The line is defined by the equation
A minimum number of 2 values is required in order to apply this regression model. The parameters arameters k and b define the slope and the offset of the line Logarithmic calculates the best fitting logarithmic curve for a given set of data. The curve is determined by the equation
The values of x and y are taken from the table graph, the parameters k0 and k1 are estimated using a least squares approximation. A minimum number of 2 values is required in order to apply this regression model. Polynomial calculates the best fit for a polynomial of order n. The order of the polynomial is restricted to values between 1 and 8. Higher orders will result in numerical instabilities. The resulting curve is determined by the following formula
Note that the minimum number of (x, y) data pairs must not be less than the n parameter. Step 2 The second step of the Fit tool wizard shows the formula of the fitting curve found. Click the Add Graph... button to add the corresponding graph. The Quality field displays the Quality-of-Fit parameter. This parameter may vary between 0.0 and 1.0, indicating the best possible fit if it equals 1.0. The quality of fit calculated by GraphSight is not adjusted to the degree of freedoms in the regression parameters.
Step 3 The third, the last Fit tool wizard page displays a set of common statistics for data (total count of data units, various kinds of mean vlues and standard deviations, correlation coefficient).
The Total units box displays the count of units in the data table. The Corelation coefficient. Generally, a correlation is the degree of association between two or more quantities. In a two-dimensional plot, the degree of correlation between the values on the two axes is quantified by the so-called correlation coefficient. GraphSight considers the correlation coefficient to be a quantity which gives the quality of a least squares fitting to the original data. This box is for displaying the value. For more information about the corelation coefficient, please refer to Weisstein, Eric W. "Correlation Coefficient." Eric Weisstein's World of Mathematics pages. The formula for the correlation coefficient calculation is
GraphSight uses the common procedure for taking the average (mean value) of a finite collection of numbers. It adds up the values, and divide by the number of terms in the sum:
The Mean X, Mean Y and Mean X-Y fields display accordingly the mean values for X, Y, and X-Y numeric vectors. A standard deviation is kind of the "mean of the mean," and often can help you find the story behind the data. To understand this concept, it can help to learn about what statisticians call normal distribution of data. A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other. The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. To learn more about the standard deviation, please refer to Robert Niles "Standard Deviation". RobertNiles.com pages.
GraphSight computes all possible kinds of standard deviation for your data. These are the Standard deviation of X, Standard deviation of Y and Standard deviation of X-Y fields.