Syntax: LLS(A, Y)
A = a range
Y = a range
LLS generates:
If any columns of A are linearly dependent, the function produces an error.
The output of LLS is a a table with four rows and n+1
columns, where n is the number of independent variables
in the model (i.e., the number of columns in the A
matrix). The table is presented in the following format:
where
= | the least squares estimate of the ith coefficient, corresponding to the independent variable in the ith column of A. | |
= | the standard error of . | |
= | the t-statistic for testing whether is significantly different from zero. | |
= | the probability of error in rejecting the null hypothesis that , based on two-sided t-test. | |
= | the mean squared error of the model. | |
MSE | = | the model coefficient of determination (the square of the model correlation coefficient, R). |
= | the t-statistic for testing whether is significantly different from zero. | |
= | the probability of error in rejecting the null hypothesis that , based on a two-sided t-test. |
Examples:
Matrix D3..E5 =
D | E | |
3 | 1 | 3 |
---|---|---|
4 | 2 | 4 |
5 | 7 | 4 |
Matrix G3..G5 =
G | |
3 | 9 |
---|---|
4 | 5 |
5 | 4 |
LLS(D3..E5, G3..G5) =
-0.76479076 | 2.2640693 | 15.308802 |
0.9516909 | 1.0921967 | 0.54349619 |
-0.80361256 | 2.0729501 | 0.49703082 |
0.56904671 | 0.2861429 | 0.60906673 |
LLS(A1..A2, B1..C2) = Error - LLS, improper dimensions
Excel function: N/A