There is one thing about multiple regression analysis which I do not understand. Lets say your model is

\(Y_{i}=\beta_{0}+\beta_{1}*x_{i1}+\beta_{2}*x_{i2}...+b_{k}*x_{ik}+\epsilon_{i}\)

The \(\epsilon\)'s are iid normally distributed with mean 0.

Then usually the output from computer packages will show a p-value for each coefficient. This p-value is for the test if this coefficient is 0 or different from 0. My professor says that it is good if all coefficients are significantly different from zero, but why is this good?

The problem is that in the test of hypothesis, is that if the null-hypothesis is rejected, we can be "sure" that the coefficient is not 0. But if the null hypothesis is not rejected, it is not a proof that the coefficient is 0. I mean, if \(H_{0}\) is rejected, we accept \(H{a}\)?, but if \(H_{0}\) is not rejected, it is not proof that \(H_{0}\) is true?

So why do we delete a coefficient from the model if it is not significantly different from 0. We have no proof that it is 0?

\(Y_{i}=\beta_{0}+\beta_{1}*x_{i1}+\beta_{2}*x_{i2}...+b_{k}*x_{ik}+\epsilon_{i}\)

The \(\epsilon\)'s are iid normally distributed with mean 0.

Then usually the output from computer packages will show a p-value for each coefficient. This p-value is for the test if this coefficient is 0 or different from 0. My professor says that it is good if all coefficients are significantly different from zero, but why is this good?

The problem is that in the test of hypothesis, is that if the null-hypothesis is rejected, we can be "sure" that the coefficient is not 0. But if the null hypothesis is not rejected, it is not a proof that the coefficient is 0. I mean, if \(H_{0}\) is rejected, we accept \(H{a}\)?, but if \(H_{0}\) is not rejected, it is not proof that \(H_{0}\) is true?

So why do we delete a coefficient from the model if it is not significantly different from 0. We have no proof that it is 0?

Last edited: