ANOVA / Regression
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July 9, 2007 at 9:55 am #47495
Kiran VarriParticipant@KiranVarri Include @KiranVarri in your post and this person will
be notified via email.Hi Guys,
Yesterday i was going through Ftest used as part of ANOVA. Hre came a curious doubt. Though i could find a point or 2 how ANOVA differes from Regression; I was not 100% clear how/why/when i will need to use ANOVA and when i need to use Regression.
Any Help will be appreciated
Kiran Varri0July 9, 2007 at 10:06 am #158370Hi Kirani,
a quick sort of explanation is that we have 3 models for our data one more specific then the next. Model 1 is that there is no difference between the averages of the different groups, model 2 that there is at least one group that is different from the others and model 3 that all the groups differ in a very specific way, the group averages are on a straight line.
We check model 2 against model 1 with ANOVA and model 3 against either model 1 or model 2 with regression.
Hope this helps
Sandor0July 9, 2007 at 10:25 am #158371
indreshParticipant@indresh Include @indresh in your post and this person will
be notified via email.To further Sandor with example to give you more clarity
Y=f(x)
Use Anova when Y is dicrete and X is continuous data. If you wanna find if there is any difference that exist between time taken to deliver (continuous) between three different couriers (discrete)
Use regression when both Y and X are continuous. Read Sandors model 3 and 1. Example : weight is dependent on age, time taken to deliver courier is dependent on distance etc
Hope this helps
Indresh0July 9, 2007 at 11:27 am #158373
Kiran VarriParticipant@KiranVarri Include @KiranVarri in your post and this person will
be notified via email.Thanks for the insight.
The details on this i found in Minitab is as follows:
Anova differs from regression in 2 ways:
1) The independent variables are Qualitative(categorial)
2) No assumption is made about the nature of the relationship.
Will appreciate if some one can elaborate on it….0July 9, 2007 at 12:00 pm #158375
ANOVA/RegressionParticipant@ANOVA/Regression Include @ANOVA/Regression in your post and this person will
be notified via email.ANOVA and Regression are all part of the general linear model. ANOVA was “invented” in the 1920s as a computationally simpler formula for regression. An ANOVA can be run as a regression with dummy variables.
0July 9, 2007 at 6:04 pm #158391The basic functioning element of the anova is simply to compare within and between variances to determine if a significant difference exists between 2 or more means.
It tells you if something is statistically different from something else. This difference may still be practically insignificant.
Regression will indicate the direction and magnitude of the of relationship between the predictor variables (ie inputs or Xs) and the response variable (ie output or Y). The ANOVA table in this case tells you only if the input was significant statistically. If not (see pvalue) then you remove it and rerun the model without it.
Note that regression can be used for any combination of data formats (variable X or Y, discrete X or Y)
It will not illuninate interactive effects in your experiment or curvlinearity (i think), although check the latter…You need DOE for this.
Good luck.0July 9, 2007 at 6:57 pm #158394
ANOVA/RegressionParticipant@ANOVA/Regression Include @ANOVA/Regression in your post and this person will
be notified via email.A few annotations to annon’s comparison of ANOVA and Regression:
The Eta squared in an ANOVA table is the same as the Rsquared in a regression analysis. The Eta/Rsquared gives you the “practical significance” as a proportion of explained variance (Factor sum of squared/Total sum of squared).
The Ftest in ANOVA tells you the statistical significance.
“Directionality” is implied in both regression and ANOVA. ANOVA was originally used in experimental data only. That is why the term “factor” is used in Minitab for example. Regression analysis was originally used for observational data and in survey research. That is why the term “predictor” is used in books talking about regression. In many cases you establish “concurrent predction”, i.e. the prediciton is not projected in the future but Variable Y is “predicted” from Variable X). So, “directionality” is not a function of the statistical formula (ANOVA vs. Regression) but of the assumptions that you make about the underlying relationship of the variables.
There is a difference between research design (experimental vs. survey) and statistical analysis (ANOVA/Regression). Interaction effects can be analyzed in Regression using survey data by multiplying two independent variables and adding them as an additional variable in the equation. If this term is significant, you can establish an interaction effect.
In general, the confusion about ANOVA and Regression has come about because the two formulas for the statistically equivalent methodologies were developed by two competing schools of thought in biometric statistics. Originally, regression was applied to observational data, ANOVA to experimental data. Since the 1970s and with the development of the general linear model, it can be shown that they are part of the same family of statistics that make the assumption that variables can be viewed as a linear combination of each other.0 
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