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Logical Line Fitting: One Step in the EDA Process

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

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Logical Line Fitting: One Step in the EDA Process

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  1. 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

  2. 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, graph the data • Focus on sense-making rather than theory

  3. 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

  4. “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)

  5. 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 3rd quartile or below the 1st quartile • Examine outliers carefully and understand their appearance in your data set • Need to decide what to do with outliers – include or discard?

  6. 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

  7. 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

  8. r2 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 • r2 is another way to assess how well the line fits the data (the closer to 1 the better the fit)

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