a-What is the shape of the sampling distribution for the parameter estimates from regression? b-Speak generally...

a-What is the shape of the sampling distribution for the parameter estimates from regression?

b-Speak generally about the process of testing the null hypothesis in the regression context.

Expert Solution

a. Sampling distribution for the parameter estimates typically follow normal distribution, so they are bell shaped.

b. In the context of regression, coefficients are the main parameters to be estimated, and it is these parameters that define regression and tell whether there is any relationship between dependent variable and independent variables.

So, the main objective of any testing in the context of regression is whether there is any relationship between dependent variable and independent variables or not.

However, these relationships (i.e. coefficients) can be negative or positive with different magnitudes. Instead of getting into all these and deciding what should be the null hypothesis, it is easier to define null hypothesis at a single point and then see whether it holds or not. If a coefficient is 0 then it means there is no relation, and if a coefficient non-zero then it means there is a relationship.

So we define null hypothesis to be,

H₀: = 0

H_a: 0

Our goal is to reject the null hypothesis in order to prove there is some relationship between dependent variable and independent variable. That is why we call a variable significant if null hypothesis is rejected.

milcah answered 5 days ago

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