I want to model data by using linear regression in which there are 4 independent and 1 dependent variables. I used ANOVA to examine an independent var but the test result showed that it is not significant(I clustered dependent var based on the levels of the independent var). I conclude that this var is not important to enter the regression model. But when I built the regression, surprisingly I saw it was significant (p-val
Babak Jamshidi it is continuous but only has 4 levels (4 values).
Keep in mind that ANOVA and regression have quite different aims. ANOVA analysis allows you to explore whether mean of one variable is significantly different from the mean of all other variables. In other words you test
mean (a) = overall mean of (b, c, d, e ....)
Very low p implies that you reject the hypo that the means are the same.
The regression analysis allows you to explore the "causal" link between the independent variables and the dependent variable and you check this variable by variable.
Thus, you can end up with different results because the type of analysis/testing is different.
Hope this helps.
The ANOVA tests whether there is a difference in the mean of the dependent variable between the four levels of the independent variable.
If you do regression analysis with the same independent variable as a categorical predictor and no other independent variables, then the result should be identical to the ANOVA.
If you do regression analysis with the same independent variable as a continuous predictor, then you test for a trend, i.e. if the dependent variable increases/decreases with the level of the independent variable.
Linear regression analysis is better suited to detect linear trends between the dependent and independent variable. Treating a numeric variable as categorical results in loss of power if the true trend is linear, but might help to detect non-linear relationships between the dependent and independent variable.
It does not seem like you include interactions in the model? Thus, saying that this variable has an important "interaction" with other variables in the model is wrong. Rather, one could say that it is significant when "controlling" for the other covariates.
Ehsan Ramezani-Khansari I would just add to the speech of Andrea Moro that one you use to check if there is a relationship (ANOVA). In particular, I always follow a sequence of statistical steps. But it is different to talk about an influencing factor and a difference in average.
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