3. A realtor is interested in predicting home selling prices in his surrounding area.
She takes a random sample of 24 homes that have sold in this area during the past
18 months, observing the selling PRICE ($y$), AREA of the house ($x_1$), number of
BEDrooms ($x_2$), number of BATHrooms ($x_3$), whether or not there is a POOL
($x_4$), and the AGE of the house in years ($x_5$). She fits the following models with
the following predictors:
• Model 1 with predictors AREA, BED, BATH, POOL, and AGE yields $SSE_1$
= 250 and $SSR_1$ = 450.
• Model 2 with predictors AREA, BATH, and POOL yields $SSE_2$ = 325 and
$SSR_2$ = 375.
In the presence of the predictors AREA, BATH, and POOL in the model, test
whether BED or AGE are significant. Use the fact that $F_{0.05,1,22} \approx 3.55$. State all
hypotheses, the test statistic, and form a conclusion in context.
