Transportation Statistics and Microsimulation

Linear Regression    ◾    189

10.2.3 Prediction

A common reason for tting a straight line is to predict the value of the

dependent variable Y from the given value of the predictor variable X.

For example, we may wish to predict travel times using measured volume

from inductance loop detectors as a predictor. For prediction individual

parameters are less important; instead, it is pertinent to know how the

estimated parameters are used together to make a prediction. e predic-

tor that we will use is

ˆ

ˆ

ˆ

.YabX=+

(10.12)

e standard error for the prediction is

ˆˆ

()

.

ˆ

σσ

Y

i

i

n

n

XX

XX

=++

−

(

)

−

=

∑

1

1

2

2

1

(10.13)

e standard error for the line used in predic