Logical Line Fitting One Step in the EDA
- Slides: 8
Logical Line Fitting: One Step in the EDA Process by Shannon Guerrero Northern Arizona University NCTM 2008 Annual Meeting & Exposition Salt Lake City, UT April 2008
EDA (Exploratory Data Analysis) Mostly graphical approach to data analysis ¡ Emphasizes uncovering underlying structure of data, extract important variables, detect outliers/anomolies, test underlying assumptions, maximize insight into data set ¡ Graph the data, graph the data ¡ Focus on sense-making rather than theory ¡
Why curve fitting? Applications in data analysis & algebra ¡ “Analyses of the relationships between two sets of measurement data are central in high school mathematics” (p. 328 NCTM PSSM) ¡ modeling, prediction, symbolic representation, correlation, regression, residuals ¡
“Line of Best Fit” Explains relationship between two variables with a straight line that “best fits” the data ¡ Line may pass through some, none, or all of the points ¡ Used to predict future values from existing values (interpolate vs extrapolate) ¡
Outliers ¡ ¡ An observation that lies outside the overall pattern of a distribution For one variable, a convenient def’n is a point that falls more than 1. 5 times the IQR above the 3 rd quartile or below the 1 st quartile Examine outliers carefully and understand their appearance in your data set Need to decide what to do with outliers – include or discard?
Curve Fitting vs. Regression Power of curve fitting often lost as we revert right to regression calculations ¡ Curve fitting is more general and an approximation ¡ Equation found (using either method) can help uncover underlying structure of data, predict future values from past ones, model causal relationships, and maximize insight into a data set ¡
Linear Regression Statistical approach to finding relationship between two variables ¡ Least squares regression attempts to minimize the squared residuals (residual – difference between observed value and value given by model) ¡ Assumption: for a fixed value of x the value of y is normally distributed with equal variations across x ¡
r 2 and residuals ¡ ¡ residual – difference between an observed value and value predicted by regression line residual plot is a scatterplot of regression residuals against the explanatory variable helps us assess fit of regression line r 2 is another way to assess how well the line fits the data (the closer to 1 the better the fit)