The purpose:to acquire skills of determination of multiple regression equation by means of MS Excel.

Laboratory work No.9

Multiple regression

The purpose: to acquire skills of determination of multiple regression equation by means of MS Excel.

The task

1. To find the multiple regression equation according to initial data of values y_i and x_ij.

2. To estimate the adequacy of received multiple regression equation.

The plan of work

1. To make matrix X in Excel and corresponding transposed matrix X^T with the help of build-in function “ТРАНСП”. Take into account that x_1j= 1.

2. To find product of received matrices X^T*X and its inverse matrix (X^T*X)^-1.

3. To make matrix Y and find the product X^T*Y.

4. To find matrix A(a_j values) as the product (X^T*X)^-1* X^T*Y.

5. To write multiple regression equation in general form using corresponding values of matrix A.

6. To make additional columns near initial data table for values “ŷ”, “(ŷ-ӯ)²”, “(y-ӯ)²”and fulfill them.

7. To find the coefficient of multiple determination according to the formula:

R² = Σ(ŷ-ӯ)²/ Σ(y-ӯ)².

And make conclusion about adequacy of received multiple regression equation.

8. To find the Fisher’s criterion for received coefficient:

F = (R²*K1) / ((1-R²)*K2), where K1 = m – 1, K2 = n – m

(n – quantity of investigation series, m – quantity of “x” parameters).

9. To find the table value of Fisher’s criterion for probability 0,05 with K1 and K2 freedom states.

10. To estimate the statistical significance of received coefficient of multiple determination R².

Дата добавления: 2015-11-04