文档介绍：第5章多元回归分析：进一步讨论
Functional Form
OLS can be used for relationships that are not strictly linear in x and y by using nb2gdppc2+u
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More on Quadratic Models
Suppose that the coefficient on x is negative and the coefficient on x2 is positive
Then y is decreasing in x at first, but will eventually turn around and be increasing in x
y
x
x*
For example: the cost function
C(Q)=b0 +b1Q+b2Q2+u
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More on Quadratic Models, Example Effects of Pollution and House Prices
Variables
price, median housing price;
nox, the amount of nitrogen oxide in the air, in parts per million;
dist, a weighted distance of the community from five employment centers, in miles;
rooms, the average number of rooms in houses in the community
Stratio, the average student-teacher ratio of schools in the community.
The estimated model
log(priĉe)=-(nox)-(dis)-+ 2-
() () () () () ()
n=506 R2=
The estimated turn point is =/(2*)=
rooms
log(price)
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Interaction Terms
For a model of the form
y = b0 + b1x1 + b2x2 + b3x1x2 + u
we can’t interpret b1 alone as measuring the change in y with respect to x1, we need to take into account b3 as well, since
Interaction term
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Interaction Terms, cont. Example: wage determinations
Model with interaction terms of educ and tenure
wage=b0+b1 educ+b2exper+ b3 tenure+b4educ×tenure+u
Estimated model with interaction terms of educ and tenure
wâge=-++-+×tenure
() () () () ()
n=526 R2=
The effect of educ on wage at the mean of tenure is
dwage/deduc=+=+×=
Whether the estimate is statistically different from zero? That is, whether b1+b4tenure (b1+b4×) is different from zero?
wage=b0+(b1 +b4×