CHAPTER 16 Getting Straight Talk on Straight-Line Regression 215

You should proceed with straight-line regression when one or more of the follow-

ing are true:»

» ^{You want to test whether there’s a statistically significant association between}

the X and Y variables.»

» ^{You want to know the value of the slope and/or intercept (also referred to as}

the Y intercept) of a line fitted through the X and Y data points.»

» ^{You want to be able to predict the value of Y if you know the value of X.}

Understanding the Basics of

Straight-Line Regression

The formula of a straight line can be written like this: Y

a

bX . This formula

breaks down this way:»

» ^{Y is the dependent variable (or outcome).»}

» ^{X is the independent variable (or predictor).»}

» ^{a is the intercept, which is the value of Y when X}

0.»

» ^{b is the slope, which is the amount Y changes when X increases by 1.}

In straight-line regression, our goal is to develop the best-fitting line for our data.

Using least-squares as a guide, the best-fitting line through a set of data is the

one that minimizes the sum of the squares (SSQ) of the residuals. Residuals are the

vertical distances of each point from the fitted line, as shown in Figure 16-2.

FIGURE 16-2:

On average, a

good-fitting line

has smaller

residuals than a

bad-fitting line.

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