Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate MathematicsHouston, Texas, November 16-19, 1995Paper C028Multiple Linear Regression Using the Matrix Capabilities of the TI-85 |
Charles BareDepartment of Mathematical Sciences Chadron State College Chadron, NE 69337 USA Phone: (308) 432-6236 cbare@csc1.csc.edu |
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ABSTRACT
The paper will begin with a brief overview of the matrix approach to least squares multiple regression. Following the introduction to least squares, matrix capabilities of the TI-85 will be demonstrated as a tool to estimate regression coefficients of several multiple regression models. After the regression coefficients have been estimated, the matrix capabilities of the TI-85 will be used for prediction and description. Examples will be included.Theoretical regression models: Linear: Y = B0 + B1X1 + B2X2 + ... + BkXk + E Power: Y = B0(X1B1)(X2B2) ... (XkBk)E Exponential: Y = B0(B1X1)(B2X2) ... (BkXk)E
Empirical linear model: Y = b0 + b1X1 + b2X2 + ... + bkXk
Data matrices: Ynx1 = [Y1, Y2, ... , Yn]T Xnx(k+1) = [1, X1, X2, ..., Xk]
Coefficient estimation: b = (XTX)-1XTY
After coefficient estimation, predicted values, mean deviations, coefficient of determination, and the multiple correlation coefficient can be easily computed with the matrix capabilities of the TI-85.
Keyword(s): statistics, TI-85