Suppose you want to test whether you can solely rely on assessment to predict house price, that is, knowing housing characteristics will not you predict housing price, once assessment is included in the model. using a sample of 125 houses, you have estimated price= α+ β1 assess+ β2 lotsize+ β3 sqrft+ β4 bdrms+ u and you decide to do a test at the 5% significance level. then your best approach to answering the question is to:
a) check each of the p-values for β2 ,β3 , and β4 . if none of them is < 0.05, you decide you don’t need the characteristics.
b) check the overall f statistic for the model. if the corresponding p-value is < 0.05, you decide you need the characteristics.
c) test the joint significance of β2 ,β3 , and β4 .that is, estimate price= α+ βassess+ u , and calculate an f statistic that is equal to (( rur− rr)/3)/((1− rur)/120) , where rur is the r2 from the first regression and rr is the r2 from this second regression. if this f statistic is > 2.68 you decide that you need the characteristics (the 5% critical value in an f distribution with df (3, 120) is 2.68).
d) do the same as in d, but the decision rule is that if the f statistic is > 2.68, don’t need the characteristics.