Simple Regression
Command: 
Math > Simple Regression... 
The command Math/Simple Regression... allows to calculate a regression between a single descriptor variable and a single response variable. Following is the list of regression functions^{(1)} which can be parametrized:
straight line 
y = kx + d 
parabolic curve 
y = a + bx + cx^{2} 
reciprocal curve 
y = 1/(a + bx) 
hyperbolic curve 
y = a + b/x 
logarithmic curve 
y = a + bln(x) 
exponential curve 
y = a e^{bx} 
polynomial curve 
y = a_{0} + Sa_{i}x^{i} 
centered polynomial 
y = a_{0} + Sa_{i}(xx_{0})^{i} 
Hoerl function 
y = k_{0}k_{1}^{x}x^{k2} 
normal distribution 

natural spline 
y = S_{k}(x) = a_{k,0} + a_{k,1}(xx_{k}) + a_{k,2}(xx_{k})^{2} + a_{k,3}(xx_{k})^{3} für x [x_{k}, x_{k+1}] und k=0,1,2...n1 
smoothed spline 
y = S_{k}(x) = a_{k,0} + a_{k,1}(xx_{k}) + a_{k,2}(xx_{k})^{2} + a_{k,3}(xx_{k})^{3} für x [x_{k}, x_{k+1}] und k=0,1,2...n1
smoothing factor γ = 0.0...1.0

Hint: 
Using data which span a small range at a large offset may lead to numeric instabilities and roundoff errors when calculating polynomial fits of higher order (this is not a deficiency of DataLab but a general problem of limited numeric accuracy in digital computers). A possible remedy to this is to use centered polynomials with the x_{0} value set to the center of the xvalues (DataLab does this automatically when selecting the "Shifted Polyn." function). 
After clicking the command, the user has first to select the input (descriptor) variable and then the response variable. Thereafter a window is displayed which allows to select among the abovementioned curve types and to calculate the corresponding parameters:
The regression results are displayed on five pages:
Regression 
On this page the plot of the data and the regression curve are shown. Data can be marked by drawing a rectangular window around the data to be marked. 
Residuals 
The residuals plotted against the descriptor are shown on this page. Again, data can be marked by drawing a rectangular window around the data to be marked. 
Distribution of Residuals 
This page shows the histogram of the residuals which the ideal normal distribution plotted on top of the historgram. 
Details 
The most important details on the regression function are shown here: the parameters of the curve, the DurbinWatson test for serial correlation among the residuals, the Lilliefors test on normality of the residuals, and the ANOVA. 
Calculate 
On this page the user may calculate values of the dependent variable for particular values of the independent variable. The confidence interval is both calculated for the means and for individual values (at a level of confidence specified by the user). 
There are several shortcut buttons left to the chart area which support the following actions:
switching the axes 

The currently selected variable can be switched by clicking the arrow buttons. The top buttons affect the dependent variable, the bottom buttons the independent variable. 
selecting new variables 

Another variable may be selected by using the eye dropper button. Clicking this button enables you to pick a particular variable by means of the variable selection dialog. 
removing marks 

Marked data can be unmarked by clicking this button. 
copying residuals 

Clicking this button allows to copy the residuals of the regression into the matrix clipboard. 
saving the regression equation 

The regression equation can be saved as a script file. Please note that the destination variable is undefined and indicated by the place holder "CX$$". 
