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MATHEMATICAL MODELING LINEAR QUADRATRIC (POLYNOMIAL) LOGISTICAL  EXPONENTIAL MULTIPLE REGRESSION
Fitting a Curve to a Scatter Plot of Data Points Regression Modeling:  From a known set of data points, (x, y), an equation of a curve is developed that “best fits” the points. The least-squares method is used to determine the best fitting equation for the specified data points. Basically, the least-squares regression technique minimizes the squared "errors" between the actual data points and the corresponding points on the curve.
Least-Squares Method the sum of the  differences in  the distances from the point  to the line is minimized resulting in an equation that best fits the given data points
Linear Regression:  Equation of a Line  Fit an equation of a line through the  points y = mx + b is the result m = slope of the line, b = y-intercept  (0, b) Methods to generate the line equation: EXCEL function (Stats -> LnReg) Calculators:  TI 83+ Internet Resources Paper and Pencil Method
Goodness of Fit A number from 0 to 1.0 (fraction) that indicates how well the curve fits the data 1.0 indicates a perfect fit 0.0 indicates no fit  Residual Error:  The difference in the predicted value of y and the actual value of y Regression analysis attempts to minimize the residual error.
Quadratic Regression Graph of data points generally follow a parabolic path Equation of parabola is a better predictor of the data

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Mathematical modeling

  • 1. MATHEMATICAL MODELING LINEAR QUADRATRIC (POLYNOMIAL) LOGISTICAL EXPONENTIAL MULTIPLE REGRESSION
  • 2. Fitting a Curve to a Scatter Plot of Data Points Regression Modeling: From a known set of data points, (x, y), an equation of a curve is developed that “best fits” the points. The least-squares method is used to determine the best fitting equation for the specified data points. Basically, the least-squares regression technique minimizes the squared "errors" between the actual data points and the corresponding points on the curve.
  • 3. Least-Squares Method the sum of the differences in the distances from the point to the line is minimized resulting in an equation that best fits the given data points
  • 4. Linear Regression: Equation of a Line Fit an equation of a line through the points y = mx + b is the result m = slope of the line, b = y-intercept (0, b) Methods to generate the line equation: EXCEL function (Stats -> LnReg) Calculators: TI 83+ Internet Resources Paper and Pencil Method
  • 5. Goodness of Fit A number from 0 to 1.0 (fraction) that indicates how well the curve fits the data 1.0 indicates a perfect fit 0.0 indicates no fit Residual Error: The difference in the predicted value of y and the actual value of y Regression analysis attempts to minimize the residual error.
  • 6. Quadratic Regression Graph of data points generally follow a parabolic path Equation of parabola is a better predictor of the data