The form of the general least squares linear regression model is:
where f_{j}(X) are any arbitrary functions of X that are called the basis functions. In regression modeling, the term 'linear' means that the models dependence on its parameters Aj is linear. The functions f_{j}(X) may be nonlinear.
The parameters A_{j} are estimated by the method of least squares.
Standard
error of the estimate:
where Xi, Yi are the data points,
n - Number of data points.
In FindGraph, linear regression model is linear combination of
Polynomial | f_{1k}(X) = ((X-X_{1})/W_{1})^k |
Rational | f_{2k}(X) = (W_{2/}(X-X_{2}))^k |
f_{3k}(X) = sqrt((X-X_{3})/W_{3}) | |
Logarithmic | f_{4k}(X) = (log ((X-X_{4})/W_{4}))^k |
Exponential | f_{5k}(X) = exp((X-X_{5})/W_{5}*k) |
Fourier | f_{6k}(X) = sin((X-X_{6})/W_{6}*k) |
f_{7k}(X) = cos((X-X_{6})/W_{6}*k) |
Parameters X_{j} and W_{j }are fixed. The parameter k varies from 1 up to 8.
FindGraph copies information about data fitting to the Log Fitting Window. To view it select menu item <View><Fitting Log>.
See examples.
See Fitting,
Interpolation.