Introduction to Statistical Methods with MATLAB
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Course Outline Exploring Data Visualize data sets, calculate descriptive group statistics, and explore data distributions. Fitting a Curve to Data Perform linear and nonlinear regression to fit a curve
Before trying to perform calculations or draw conclusions from data, it is helpful to get a qualitative feel for the data. Visualization is often a useful method when beginning to
Measures of Centrality From the histograms of height data shown to the right, it appears that women’s heights are centered on approximately 160 cm, whereasmen’s heights are centered on approximately
Histograms and Data Distributions A histogram can give a qualitative feel for the shape of a data set. The exact shape of the distribution is given by the distribution’s probability
Visualizing Data histogram Bar plot of frequencies of data values. boxplot Box-and-whisker plot based on median and quartiles. scatter Plot relationship between two variables. Measures of Centrality and Spread Mean
Suppose you suspect there is a relationship between two variables, x and y. The simplest relationship (and the one you can usually assume as a starting point) is that of a straight line,or y=ax+b.
How Well Does the Curve Fit the Data? There are many ways of evaluating the quality of a fit. The fit function returns information on the quality of the fit
Linear vs. Nonlinear Linear regression can fit a nonlinear curve to the data, as long as the model is linear in the coefficients, or parameters. For example, fitting a cubic
Linear and Nonlinear Regression The fit function can perform linear or nonlinear regression. Linear regression is when the model is linear in the parameters. For example: Y=p1x3+p2x2+p3x+p4 Otherwise, the regression is
Additional Interpolation Methods Linear interpolation gives a simple, continuous interpolant, but it may not be appropriate for all data sets. The interp1 function allows for a fourth input to specify
Summary: Interpolating Data Interpolation Methods for interp1 method Interpolation method used 'linear' [Default] Linear interpolation. 'spline' Cubic spline interpolation. 'pchip' Cubic polynomial interpolation preserving increasing/decreasing property of data. 'next'