![]() ![]() To illustrate why the standard error of the regression can be a more useful metric in assessing the “fit” of a model, consider another example dataset that shows how many hours 12 students studied per day for a month leading up to an important exam along with their exam score: If we’re interested in making predictions using the regression model, the standard error of the regression can be a more useful metric to know than R-squared because it gives us an idea of how precise our predictions will be in terms of units. Roughly 95% of the observation should fall within +/- two standard error of the regression, which is a quick approximation of a 95% prediction interval. The standard error of the regression is particularly useful because it can be used to assess the precision of predictions. But on average, the observed values fall 4.19 units from the regression line. Notice that some observations fall very close to the regression line, while others are not quite as close. If we plot the actual data points along with the regression line, we can see this more clearly: In this case, the observed values fall an average of 4.89 units from the regression line. The standard error of the regression is the average distance that the observed values fall from the regression line. In this case, 65.76% of the variance in the exam scores can be explained by the number of hours spent studying. R-squared is the proportion of the variance in the response variable that can be explained by the predictor variable. If we fit a simple linear regression model to this dataset in Excel, we receive the following output: Suppose we have a simple dataset that shows how many hours 12 students studied per day for a month leading up to an important exam along with their exam score: This tutorial explains how to interpret the standard error of the regression (S) as well as why it may provide more useful information than R 2. Two metrics commonly used to measure goodness-of-fit include R-squared (R 2) and the standard error of the regression, often denoted S. To view up to date information on the project.When we fit a regression model to a dataset, we’re often interested in how well the regression model “fits” the dataset. elegans is affected by how constrained their motion is, meaning whether they are crawling, slipping/sliding, or actually swimming. Diffraction Pattern Waveform taken from the Oscilloscope Dataīased on initial frequency values it would appear the thrashing frequency of C. The automated technique also appears to reveal information about the worm shape as it is moving through the laser beam. The logger pro method was fairly time intensive, so an automated technique using a oscilloscope connected the the computer was developed to allow for a faster analysis and determination of thrashing frequency. Example of a Logger Pro graph of angular frequency vs. This video data was analyzed using logger pro and the average thrashing frequency and standard deviation was determined for each cuvette. The density of worms in the cuvettes was also controlled and more video data was taken. Next more control was exerted over how much space the worms had to move by using 1mm, 2mm, and 5mm cuvettes. Matlab Modeled Worm Orientation and Resulting Diffraction Image Actual Image of a Diffraction Pattern taken from the Video Data Matlab was used to model the possible orientations of the worms and the fast Fourier Transform of the model worms resulted in a modeled diffraction pattern that could be compared to the raw video data. Initially video data of the diffraction patterns of the worms was taken. Initial Diffraction Data Collection Set-Up ![]() elegans can be used to study the movement and position of the worms as the pass through the beam of light. The diffraction patterns created by a laser beam traveling through an optical cuvette of C. The dynamic diffraction analysis began as a project to determine whether a three-dimensional technique using laser light to study biological systems could be an inexpensive and accurate alternative to microscopy. Pages written by Michael Lueckheide ’13 Dynamic Diffraction Analysis
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