Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate Mathematics

Houston, Texas, November 16-19, 1995

Paper C028

Multiple Linear Regression Using the Matrix Capabilities of the TI-85

Charles Bare

Department of Mathematical Sciences
Chadron State College
Chadron, NE 69337
Phone: (308) 432-6236

Click to access this paper: paper.pdf


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