Dear Abraham,

For the first one you can go with ANOVA , for the second one you may try  ANCOVA. 

For third one, if your dependent and independent variables are continuous, you can go for regression model. But you need to check whether linear or non-linear modeling is appropriate after studying the relation between dependent and independent variables. If your dependent variable categorical and independent variable is continuous and/or categorical, you can go with logistic regression. If your dependent variable is continuous and some of the independent variables are categorical, you can go with regression modeling using dummy variables. 

Marian -

You should probably break this into several questions to pursue individually.  

I'd not use "significance," but rather a confidence interval around a difference in means, which is far more usefully interpretable. See the following:

Press release for the American Statistical Association:

http://www.amstat.org/newsroom/pressreleases/P-ValueStatement.pdf

My letter to ASA:

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

Independent (regressor) variables interact with one another such that it is often not very helpful to try to look at them in isolation.  You could go into a big discussion of this, and would best be more specific about what you want to know.

Different types of data call for different types of regression (as noted by Anush, I see). For continuous data alone, my area, the regression considerations are extensive, including linearity/nonlinearity, heteroscedasticity, and collinearity.  Again, there is enough to discuss to fill books. 

Sample size considerations are important.

Cheers  -  Jim

Article Practical Interpretation of Hypothesis Tests - letter to the...

Hi James & Anush,

Thank you so much for your detailed inputs and references.. They have been very helpful.. If you'll know of  any  reference for the third issue, please suggest..

Thanks once again 

Marian -

Besides linear and nonlinear regression for continuous data, you need to consider binomial  (yes/no) data, and (event) count data.  It depends on what you need to do, and the kind of data you have. 

You could research linear and nonlinear regression, poisson regression, logit and probit regression, and more.  Most is outside of my areas of expertise. 

There are a number of good resources on the internet, such as those for online study by the Pennsylvania State University.  One example might be this one for logistic regression I found (but I've never used, as I worked primarily with continuous data): 

 https://onlinecourses.science.psu.edu/stat504/node/149

The standard text may still be

Norman R. Draper, Harry Smith(1998), Applied Regression Analysis, 3rd Edition, Wiley. 

There is also this, which is very good:

Applied Regression Analysis and Generalized Linear Models, 2nd ed, 2008, John Fox, Sage, 

and a specialized book I like, if it might happen to cover anything you need, would be

Carroll and Ruppert(1988), Transformation and Weighting in Regression, Chapman & Hall, Ltd. London, UK.

It has good information on heteroscedasticity.  As far as transformations go, in general, however, if you can avoid them, that tends to simplify interpretation, I'd say.  Without good interpretation of results, usefulness suffers.  Hint: scatterplots often promote insight for continuous data, though spurious results can occur, and subject matter theory needs to be considered. 

You need to consider variance (often too many variables), bias (possibly important omitted variables), heteroscedasticity, whether or not an intercept term is useful, and for areas outside of the cross-sectional data I primarily used, autocorrelation, and I suppose there are other considerations.   I did little with time series.

For multiple regression, there are various ways that regressors (independent variables) might interact,  which could cause problems. 

Hope you find something helpful.  There is a lot to consider.  Perhaps you could find a copy of Draper and Smith, and look for online help, such as from Pennsylvania State University webpages, or the (US) National Institutes of Health (NIH). 

Cheers - Jim

Thanks a lot James for these references and inputs for my problem. I will surely check out Draper & Smith, (1998)

Thanks once again