a. Find OE(y x)/ox, and comment on how it depends on x. b. Show that & is equal to dE(y|x)/0x averaged across the distribution of x. c. Suppose that x has a symmetric distribution, so that E[(x- =0. Show that L(y|1, x) = 20 +dx for some 2o. Therefore, the coefficient on x in the linear pro- jection of y on (1,x) measures something useful in the nonlinear model for E(y|x): it is the partial effect @E(y|x)/dx averaged across the distribution of x.
a. Find OE(y x)/ox, and comment on how it depends on x. b. Show that & is equal to dE(y|x)/0x averaged across the distribution of x. c. Suppose that x has a symmetric distribution, so that E[(x- =0. Show that L(y|1, x) = 20 +dx for some 2o. Therefore, the coefficient on x in the linear pro- jection of y on (1,x) measures something useful in the nonlinear model for E(y|x): it is the partial effect @E(y|x)/dx averaged across the distribution of x.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![2.2. Let y andx be scalars such that
E(y|x) = 8o + 81(x - 4) + 82(x – 4)²,
where u= E(x).
a. Find @E(y x)/ôx, and comment on how it depends on x.
b. Show that d is equal to E(y|x)/0x averaged across the distribution of x.
c. Suppose that x has a symmetric distribution, so that E(x- 4)°] = 0. Show that
L(y|1, x) = 40 +ojx for some 2. Therefore, the coefficient on x in the lincar pro-
jection of y on (1,x) measures something useful in the nonlinear model for E(y|x): it
is the partial effect 0E(y|x)/dx averaged across the distribution of x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fbd106b-ec44-45b8-a881-a985700541b4%2Fe311bbb7-0ba0-476e-b85c-cc36c444bddf%2Fobb9d6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.2. Let y andx be scalars such that
E(y|x) = 8o + 81(x - 4) + 82(x – 4)²,
where u= E(x).
a. Find @E(y x)/ôx, and comment on how it depends on x.
b. Show that d is equal to E(y|x)/0x averaged across the distribution of x.
c. Suppose that x has a symmetric distribution, so that E(x- 4)°] = 0. Show that
L(y|1, x) = 40 +ojx for some 2. Therefore, the coefficient on x in the lincar pro-
jection of y on (1,x) measures something useful in the nonlinear model for E(y|x): it
is the partial effect 0E(y|x)/dx averaged across the distribution of x.
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