# If a variable is found with p-value greater than 0.05, why is it also taken for calculation in the regression equation Y=a+b1*X1+b2*X2?

Suppose, I have performed multiple regression analysis on the following data set where X1 and X2 are independent variables and Y is the dependent variable.

And achieved the following multiple regression analysis table from where it is clear that X2 is not correlated with Y as the p-value is greater than 0.05 which is 0.108 for X2 variable

So, if p value is greater than 0.05 for a variable, then why it is considered in regression equation

Y = 2.709 + 0.763(X1) + 0.463(X2) which has been shown in any online multiple regression equation calculator.

My question is Why it is not like the following Y = 2.709 + 0.763(X1) omitting the [0.463(X2)] part from the equation, as X2 is not correlated with Y

• if p value is greater than 0.05 for a variable, then why it is considered in regression equation ? It is a mythical manner, to conclude a positive or negative relationship between two postulates. – Subhash C. Davar Apr 28 '18 at 5:46

One reason to keep $X_2$ in the model is (lack of) power:
The non-rejection implied by $p>0.05$ may be a type-II error, i.e., a wrong null hypothesis of irrelevance of $X_2$ that has wrongly not been rejected. Especially in situations like yours where the sample size is small, such problems may occur often.
Put somewhat differently, while the effect of $X_2$ is not statistically significant, it may still be significant from a subject matter point of view - 0.463 may be a "large" effect which we just may not be able to statistically distinguish from zero given the estimation uncertainty.
Also, note that, in any case, it would not be sound to report $Y = 2.709 + 0.763X_1$ as your fitted model. If you drop $X_2$ and reestimate your model with only $X_1$ as a regressor, the coefficient estimates will differ.