ENG 6 Lecture Notes - Lecture 10: Standard Deviation, C Mathematical Functions, Torsion Spring
Document Summary
Least squares regression: minimizes area between data and line you predict. Polyval: takes coefficients of polynomial (for example, from polyfit) and a vector of x points to evaluate at that polynomial. Regression example: linear fit: torque needed to turn torsion spring of mousetrap through an angle is given in data points, find constants for model given by t = k1 + k2x. >> plot(xp,yp,"o"); hold on; plot(xfit,yfit); hold off; Interpolation or regression: for acceleration/velocity/distance problems, need to differentiate and integrate, best to fit a known function that can be easily differentiated or integrated, use a spline fit. Physics of gravity tells us that it should follow a smooth curve. Gives us just one function to work with. Fitting to more complicated functions: linearizing: making a few substitutions for variables which result in an equation for a line. Linear vs. nonlinear fitting: linear in terms of fitting constants: Y = a + bt + ct^2.
