Texas Instruments TI-89 User Manual - Page 943
Regression Formulas
UPC - 033317196326
View all Texas Instruments TI-89 manuals
Add to My Manuals
Save this manual to your list of manuals |
Page 943 highlights
Regression Formulas This section describes how the statistical regressions are calculated. Least-Squares Algorithm Most of the regressions use non-linear recursive least-squares techniques to optimize the following cost function, which is the sum of the squares of the residual errors: N ∑ J = [residualExpression] 2 i =1 where:residualExpression is in terms of xi and yi xi is the independent variable list yi is the dependent variable list N is the dimension of the lists This technique attempts to recursively estimate the constants in the model expression to make J as small as possible. For example, y=a sin(bx+c)+d is the model equation for SinReg. So its residual expression is: a sin(bxi+c)+d" yi For SinReg, therefore, the least-squares algorithm finds the constants a, b, c, and d that minimize the function: N ∑[ ] J = a sin(bxi + c) + d − yi 2 i =1 Regressions Regression Description CubicReg Uses the least-squares algorithm to fit the thirdorder polynomial: y=ax3+bx2+cx+d For four data points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four data points are required. ExpReg Uses the least-squares algorithm and transformed values x and ln(y) to fit the model equation: y=abx LinReg Uses the least-squares algorithm to fit the model equation: y=ax+b where a is the slope and b is the y-intercept. Appendix B: Technical Reference 936