Despite the fact that many phenomenon in physical or social sciences involve interaction between causal factors, it seems that very few researchers using multiple regression or structural equation modeling techniques do investigate for the presence of those interactions. If fact, in the context of multiple regression, a statistically significant interaction is often perceived as a curse by researchers, as something that jeopardize their effort to identify simple causal factors.
This perception is somewhat reinforced by the fact that many statistical textbooks refer to a statistically significant interaction solely as an indication that an important assumption of multiple regression has been violated (namely the additivity assumption) without further instruction on how to deal with such an interaction. Some of those textbooks even suggest that the net result of such a significant interaction is that the regression model become uninterpretable. Nothing is farther from the truth!
Part of this misconception is caused by a lack of understanding of what interaction is all about and by an unfamiliarity with how interaction should be interpreted. While it is perfectly possible to deduce the nature of the interaction simply by examining the resulting regression equation, a common way to get an intuitive feel for the interaction is to compute several regression slopes relating one of the independent variable to the dependent variable at different values of the other independent variable. However, this task is cumbersome especially when investigating several possible interactions.
The ITALASSI application was developed to be a free program that has been written to facilitate interpretation of regression models (2 independent variables) with an interaction term.
The program allows you to enter several regression models (two bivariate, one multiple additive, and one multivariate with interaction) in the form of equations or compute those equations from raw data and displays the various models using 2D and 3D graphs. The program may also be used in advanced stat courses to illustrate statistical interactions or applied multiple regression. 
NOTE:
Free for personal or teaching perpose

ITALASSI is a free program that reads 2 linear regression equations in the form of an
equation (for example: y=a+bx1+cx2), or a table with both x1 and x2 values, calculates the regression
slope of the model as a function of the value of x2, and displays the slope, intercept, and standard
error of the slope. The program may be used to help interpret the regression results in 2 variables. The results of several equations (two bivariate, one multiple additive, and one multivariate with interaction) may be displayed using 2D and 3D graphs. Further, the slope of the equation
may be displayed as a function of the value of either x1 or x2. The user may display the regression results for a varying value of x1 or x2 by simply entering the value of that variable. The program has a comprehensive help text,
and can be obtained on diskette or downloaded.

Your requirements
The ITALASSI requires the specification of 2 linear regressions, each of which may have an interaction term. Usually the equations would be formulated in the following format: y=a+bx1+cx2 where x1 is the independent variable, x2 is the other independent variable and y is the dependent variable.
An example of two equations with interaction, both formulated in the typical format: y=a+bx1+cx2+dx1x2 where x1 is the independent variable, x2 is the other independent variable and y is the dependent variable, would be:
For equation 1: y=0.10-0.01x1+0.09x2+0.04dx1x2
For equation 2: y=0.05-0.01x1+0.15x2+0.05dx1x2
The program requires the use of regression equations to compute regression slopes as a function of either x2 or x1 values. The outcome of ITALASSI is a relation between a regression slope as a function of either x2 or x1, and the corresponding regression slope(s) for the other independent variable, in which an interaction is involved.

Q:

MySQL: Get the total sum of an ID column

I have this table (dont know if I am doing this right):
------------------------------------------
| ID | Amount | ID

ITALASSI is an interactive application for multivariate regression. It was developed to help researchers and students get more insight into multiple regression models. It is implemented in C++ using MFC.

What ITALASSI does?
Analyze several regression models.
Graphing of graphs and statistical representation of results.
Easily build and test regression models.

What ITALASSI does not do?
Perform model diagnostics.
Compute estimates of unknown parameters (e. g. intercept, slope,
interaction term)

Installing ITALASSI

Compiling ITALASSI
The first step is to have a Microsoft Visual C++ compiler for Windows

Get the latest version of the "Microsoft Visual C++ Compiler for
Windows"; install the latest version of the compiler available.

If you have access to a C++ compiler that does not come with the
Microsoft Visual C++ Compiler, follow this link:

Get the latest version of the "MinGW C++ Compiler"; install the latest version of the compiler available.

If you need to configure the compiler to build and run your program:

Open Visual C++.
Select Tools / Options.
In the list of settings, select the "General" tab.
In the "Command-line options" section, select "/T".
Click OK.

This will replace all of the compiler switches ( /cx, /f, /fp,
/Z7, /Zc:inline) and options ( /nologo, /o, /Ob2, /openmp,
/RTC1, /MD, /MP, /MT, /Gy, /GF, /W1, /GS) by a single switch
(/T). This setting will cause the C++ compiler to be invoked by
gcc, instead of by Microsoft Visual C++ Compiler.

Compile your code
 Get a program directory. 
 Create a debug/release directory in that program directory. 
 Open Visual C++ and select Debug /
"Application" / "C++ Application" / "Win32
Application" / "Program"
/ "Untitled1". 
 Click "Start". 
 In the Visual C++ environment's main menu, select "File" /
"New".
b7e8fdf5c8

Using the model formulae, you can enter several regression models in the form of equations or compute those equations from raw data.
The various models are displayed using 2D graphs.
A 3D plot of the scatter diagram may be generated by the program.
The program may be used in advanced statistical courses to illustrate statistical interactions or multiple regression.

Various commands, tutorials, and examples are provided in the program.

Simulate data sets.
Fit a regression model using the multiple additive modeling approach.
Fit a regression model using the multivariate modeling approach and analyze the coefficients using SPSS.
Fit a regression model using the multiple regression modeling approach and analyze the coefficients and standard errors in SPSS.
Fit several regression models with and without an interaction.
Fit a regression model with multiple additive modeling approach and fit with the optimized parameters.
Fit a multiple regression model using the interaction modeling approach and analyze the coefficients and standard errors in SPSS.

To achieve maximum potential, the user may use the raw data created by the program to simulate new data and use that data to estimate new models using SPSS.

The program requires some basic understanding of statistical regression models and some programming skills.
Note: The license for this application is single user/single machine.

References

SPSS Manual
Hairer, M., (1990), An Analysis of Interactions, Cambridge University Press, Chapter 11.

Category:Statistical modeling
Category:InteractionsGonadotropin-releasing hormone induces a Ca2+ response and a tyrosine phosphorylation of microtubule-associated protein 2 in rat hypothalamic astrocytes: specificity of the response.
The rat gonadotropin-releasing hormone (GnRH) receptor couples to multiple intracellular pathways. The peptide GnRH induces (1) a rapid increase of the intracellular calcium [Ca2+]i in a population of cultured hypothalamic astrocytes, (2) the release of lactate from astrocytes, (3) the activation of mitogen-activated protein kinase (MAPK) in these cells, (4) the release of endothelin-1 in hypothalamic endothelial cells, and (5) the opening of a nonselective cation channel in these cells. We now show that GnRH induces a rapid and transient increase of the [Ca2+]i in cultured

ITALASSI stands for Interaction Analysis and Software.
The two main targets of the program are to facilitate the identification of interaction among independent variables and to plot their effects for two or more independent variables.
The original name of the program was Interaction, but it was changed because there was no software that allowed the user to
simultaneously plot the different independent variables. For this reason, the user must enter multiple equations
into the model.
However, in this case, the first independent variable, Y, is a function of X1 and X2, which are functions of the second independent variable, Z. Thus, the first model is:
    Y = a + b + c + d + e + X2(Z)
That is, the function Y(Z) is regressed using the independent variables X1, X2, Z.
The user enters the independent variables and values for the dependent variables and then selects values for one of the independent variables, X2(Z), before calculating Y(Z) for each pair of values for the two independent variables. This can be done using the 2D graph (see example below) or the 3D graph.
The program then plots all of the functions obtained by plotting the Y-versus-X1(Z), Y-versus-X2(Z), and Y-versus-X1(Z) values for a range of Z values.
The 2D graph is limited by the constraint that only 3 values of Z can be plotted in one set of bars, and this graph cannot differentiate two or more functions. The 3D graph can contain up to 5 bars and distinguish between two and three functions (an XY-graph).
It is possible to obtain any type of function from the simplest one (linear) to the most complex function (quadratic polynomial).

See also
Multicollinearity
"Econometrics and the interaction analysis"

References

Category:Mathematical modeling
Category:Regression analysis

de:Interaktion#In Interaktion
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