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# The Reliability of Regression-Based Decisions

## 16.0. Introduction: What Is the Issue?

You have data on 108 apartments sold in Deepwater Bay in 1995. There is a clear positive association between sale price and area. The correlation is 0.828 and the least squares regression line is

There are various reasons why this regression equation might be useful. In this particular example, it can answer at least three pertinent questions.

What is the value of an extra 100ft2 of floor space? The branch office is having a sales review. Even though there was no apartment of exactly 1500ft2 in their database, what is the fair market price for such apartments? A client comes into the office with an apartment of a certain size and wants you to quote a range for likely sale price. What do you quote?

It is quite easy to give numerical answers to these questions. However, a proper statistical answer will not only give a best estimate, but will also evaluate the accuracy of this estimate. These accuracy estimates depend on the assumptions of the regression model. So a really thorough statistical answer would also verify the appropriateness of these assumptions.

## 16.1. Three Kinds of Questions That Regression Answers

Suppose that we have two business variables X and Y and are mainly interested ...

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