Tests and Confidence Regions

Abstract

Consider the example of house prices that we saw in the last chapter. It is reasonable to ask one or more of the following questions:

• (a) Is the selling price affected by the number of rooms in a house, given that the other independent variables (e.g., floor area, lot size) remain the same?

• (b) Suppose the realtor says that adding a garage will add $5000 to the selling price of the house. Can this be true?

• (c) Do lot size and floor area affect the price equally?

• (d) Does either lot size or floor area have any effect on prices?

• (e) Can it be true that storm windows add $6000 and a garage adds $4000 to the price of a house?

For some data sets we may even be interested in seeing whether all the independent variables together have any effect on the response variable. In the first part of this chapter we consider such testing problems. In the second part of the chapter we shall study the related issue of determining confidence intervals and regions. In the last section we return to testing.