If you are engaged in hypothesis testing with regression analysis, I think you need to include all variables in your report of the regression results, both significant and non-significant.

One problem with reporting the p-values for all the variables (including the non-significant ones) is that the results may be misleading because of the correlation of the independent variables.

Let’s imagine a case where the dependent variable is the amount corn grows each week, two of the independent variables are month-of-the-year and average-air-temperature-for-the-week. Both will be predictive of the amount corn grows, but they will likely be highly correlated. In our case, maybe average-air-temperature-for-the-week will be significant and month-of-the-year will not.

But we may not to mislead our readers into thinking that month is not a good predictor. Which variable ends up being significant may have to do with which one is a better predictor, or may have to do with which one was entered into the model first.

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One solution to the problem of having correlated independent variables is to report the simple correlation of the independent variable and the dependent variable.  This is in addition to the final regression model (with only significant variables, or the best model by AIC, BIC, etc.). 

This lets the read see the simple correlations, which may be informative.

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SOME OTHER OPTIONAL ADVICE...

One piece of advice is look at the correlations among your variables, both graphically and statistically.  E.g., http://rcompanion.org/handbook/images/image136.png .   This allows to see 1) Which variables are correlated simply to the dependent variable.  2) Which independent variables are correlated to other independent variables. And 3) If the correlations are more or less linear.

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A second piece of advice is to familiarize yourself with goodness-of-fit measures like AIC, AICc, and BIC.  There are others as well.

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Sometimes we want a relatively parsimonious model.  That is, one which predicts the outcome variable well, but doesn’t have too many terms. 

One option is to use p-values, but this may depend on which models are entered into the model first (depending on how the sum of squares are calculated.)

Another is to use something like AIC or BIC to balance the predictive power of the model with the number of terms used.

I feel you need to all the variables and conclude with your model with six or seven variables. 

Professor,

There is one more option where you can group 4-5 variable into a parameter and develop the hypothesis related to the effect of this parameter on the dependent variable.

For ex: Hypothesis is " Changes in process parameters affects the properties of the end product" . The process parameters have several variables like temperature, pressure, duration of the process etc. Within the process parameters, you can mention which one has significant influence and which variable has least significance.

I think you are in right way. You can start with all six variables and end up with four variable recommendation. 

In healthcare, you often get the problem where there is readily available administrative data, such as age, gender and diagnosis. Age is an estimate of biological age, gender is an estimate of genetic factors and diagnosis is a very poor estimate of acuity. Hence models to predict standardized hospital mortality can pass all the statistical tests yet at the same time be very wrong. So I would expect that you give some thought to the strengths and limitations of the variables you have chosen. Also remember than in regression fitting the data is supposed to be equally spaced. If the data is clustered the regression can give anything from good to poor results hidden behind supposed 'good' p values.

One of the fundamental assumptions of regression is that your independent variables are uncorrelated.  In Salvatore S. Mangiafico's example above where one independent variable is correlated to another, you cannot proceed with regression (leave alone reporting p-value) without resolution of multi-collinearity.  So you need to first resolve that using a factor analysis.

If your independent variables are not correlated, all of them will figure in your initial conceptual framework and the p-values of all variables need to be reported.  Altering your hypotheses after data analysis is certainly not correct - equivalent to finding a solution first and looking for a question afterwards!!

Hope this helps although a bit late in the day :-(

First, you have to incorporate stepwise regression or backward regression to find the significant factors contributing to your model.Professionally you have to write only the hypothesis based on the final model however you can disclose the significance of other factors in the conclusion part.   

Jochen Wilhelm

Thank you for your reply.

Thank you, Jochen Wilhelm