Why is having high p-value makes dependent variable significant in backward elimination? In backward elimination, I heard the steps of fitting the model by keep removing the highest p-value(a.k.a. insignificant independent variable) each time like below


  
  Select a significance level to stay in the model(e.g. SL = 0.05)
  Fit the full model with all possible predictors
  Consider the predictor with the highest P-Value(P > SL)
  Remove the predictor
  Fit model without this variable (Repeat step 3-5 until P &lt;= SL)
  


But the part which I don't get is why is having higher p-value makes the corresponding independent variable insignificant. Doesn't having high p-value mean it's more close to the null hypothesis so that that variable is more significant?
Actually, the Null Hypothesis is that the predictor is not significant. Taken from the book Introduction to Statistical Learning:


Null Hypothesis: There is no relationship between X and Y
Alternative Hypothesis: There is some relationship between X and Y


If we have a high p-value, we have an expressive result showing that the null hypothesis is correct and therefore the estimated coefficient come from a normal distribution around zero and can be discarded. I hope this answer your question, please let any comment if you need more help.