Question

Hello, I am wondering what should my Ho and Ha be in this case and what should i do to carry out the test

Test whether size is an effective predictor of house prices in the regression model. State your
null and alternative hypotheses and report the test statistic, decision rule, and conclusion to
the test. [2 marks]

Answer 1

Suppose Y done house prices and X denote size of the house.

Since there are no other information available , we will not take any more predictor variables.

Let the model be : where random variable and are regression parameter.

Want to test whether size is an effective predictor of house prices in the regression model

So

This is the hypothesis that you should take.

As for the test statistic you could either take the t statistic or the F statistic as your choice and carryout the test accordingly.

Thumb Rule of taking null :

Take the complement statement as your null. Like here "size is an effective predictor" complement of that statement is "size is not an effective predictor" so size will have no effect on house prices. Which implies that in the population this is your null hypothesis.