You're using a version of Internet Explorer that isn't supported by Questia.
To get a better experience, go to one of these sites and get the latest

# Methods of Correlation and Regression Analysis, Linear and Curvilinear

By Mordecai Ezekiel; Karl A. Fox | Go to book overview

CHAPTER 6
Determining the way one variable changes when another changes: (3) for curvilinear functions

A straight-line equation is frequently a fairly good empirical statement of the relation between two variables even when the true relation is more complex than the straight line can portray. Yet it maybe just as important to know the exact or approximate "form" of the relationship as it is to have an empirical statement of it. For that reason it is necessary to consider other ways of expressing a relationship than the straight line.

The automobile-stopping case (Figures 4.1 and 4.2) showed that the relations could not be well expressed by a straight line, especially below 15 miles per hour, and above 35. The latter might be very important for the purpose of the whole study.

The real difficulty involved would have been the assumption that the straight-line function applied. That would have assumed that an increase of one mile in the speed of the car increased the distance required for stopping by the same number of feet, no matter how fast the car was already traveling. When we examine Figures 4.1 and 4.2 closely, we see that this is not correct; the line of averages slants up slowly at first, then tends to rise more steeply as the speed is increased, until it has the steepest slope at the highest speed. It is therefore incorrect to assume that we can express the slope of the line by determining the average increase in stopping distance for an increase of one mile in the rate of speed; for the increase in stopping distance is not the same regardless of the rate of speed, but tends to become greater as the rate of speed increases. Only if our way of stating the line can express that fact too will it sum up all our observations with sufficient accuracy.

What is needed is some general way of stating the relation between

-69-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Project items

#### Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Methods of Correlation and Regression Analysis, Linear and Curvilinear

Settings

Typeface
Text size
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Full screen
/ 550

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.