Collinearity refers to linear relationships between two X variables. Multicollinearity encompasses
linear relationships between more than two X variables. Multiple regression is impossible in the
presence of perfect collinearity or multicollinearity. If X1 and X2 have no independent variation, we
cannot estimate the effects of X1 adjusting for X2 or vice versa. One of the variables must be
dropped. This is no loss, since a perfect relationship implies perfect redundancy. Perfect
multicollinearity is, however, rarely practice problem.
the generation of ultrashort laser pulses. Beginning with mode-locking of
glass lasers in the 1960s, the development of dye lasers brought the pulse
width down from picoseconds to femtoseconds. The breakthrough in solid
state laser pulse generation provided the current reliable table-top laser
systems capable of average power of about 1 watt, and peak power density
of easily watts per square centimeter, with pulse widths in the
range of four to eight femtoseconds.
dipole antenna is a radio antenna that can be made of a simple wire, with a center-fed
driven element. It consists of two metal conductors of rod or wire, oriented parallel and
collinear with each other (in line with each other), with a small space between them. The
radio frequency voltage is applied to the antenna at the center, between the two
conductors. These antennas are the simplest practical antennas from a theoretical point of
The characteristicsof a vector are the magnitude, the orientation, and
the sense. The magnitudeof a vector is speci®ed by a positive
number and a unit having appropriate dimensions. No unit is stated if
the dimensions are those of a pure number. The orientationof a vector is
speci®ed by the relationship between the vector and given reference lines
and=or planes. Thesenseof a vector is speci®ed by the order of two points
on a line parallel to the vector. Orientation and sense together determine the
directionof a vector.
The EyeTap glasses of the previous chapter absorb and quantify rays of light, process these rays of light, and then resynthesize corresponding rays of light. Each synthesized ray of light is collinear with, and responsive to, a corresponding absorbed ray of light. The exact manner in which it is responsive is the subject of this chapter. In other words, this chapter provides meaning to the word “quantify” in the phrase “absorb and quantify.
In column III we additionally look at the age composition of popula-
tion. We add two variables, namely the percentage of population that is
below 14 and the percentage of population that is between 14 and 64 years
old. Note that the share of elderly people above 64 years cannot be
simultaneously added as the three shares add up to one and are therefore
collinear. Adding the age composition hardly affects the population elas-
ticity, which remains close to unity.
A polygon is a plane figure bounded by a closed broken line. i.e.. a line obtained if one takes n distinct points such that no three successive points are collinear and draws a straight line segment between each of these points and its successor as well as between the last point and the first point (Fig. 3.13d).