Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y = Bo + dod + Biz + did•z + u; this is a general version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17).] (i) Because it changes nothing important, set the error to zero, u = 0. Then, when d = 0 we can write the relationship between y and z as the function fo(z) = Bo + Biz. Write the same relationship when d = 1, where you should use fi(z) on the left-hand side to denote the linear function of z. (ii) Assuming that & + 0 (which means the two lines are not parallel), show that the value of z* such that fo(z*) = fi(z*) is z* = -dg/ô1. This is the point at which the two lines intersect [as in Figure 7.2 (b)]. Argue that z* is positive if and only if 8o and &, have opposite signs. (iii) Using the data in TWOYEAR, the following equation can be estimated: log(wage) = 2.289 – .357 female + .50 totcoll + .030 female · totcoll (.005) (0.011) (.015) n = 6,763, R² = .202, (.003) where all coefficients and standard errors have been rounded to three decimal places. Using this equation, find the value of totcoll such that the predicted values of log(wage) are the same for men and women. (iv) Based on the equation in part (iii), can women realistically get enough years of college so that their earnings catch up to those of men? Explain.
Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y = Bo + dod + Biz + did•z + u; this is a general version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17).] (i) Because it changes nothing important, set the error to zero, u = 0. Then, when d = 0 we can write the relationship between y and z as the function fo(z) = Bo + Biz. Write the same relationship when d = 1, where you should use fi(z) on the left-hand side to denote the linear function of z. (ii) Assuming that & + 0 (which means the two lines are not parallel), show that the value of z* such that fo(z*) = fi(z*) is z* = -dg/ô1. This is the point at which the two lines intersect [as in Figure 7.2 (b)]. Argue that z* is positive if and only if 8o and &, have opposite signs. (iii) Using the data in TWOYEAR, the following equation can be estimated: log(wage) = 2.289 – .357 female + .50 totcoll + .030 female · totcoll (.005) (0.011) (.015) n = 6,763, R² = .202, (.003) where all coefficients and standard errors have been rounded to three decimal places. Using this equation, find the value of totcoll such that the predicted values of log(wage) are the same for men and women. (iv) Based on the equation in part (iii), can women realistically get enough years of college so that their earnings catch up to those of men? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model
y = Bo + dod + Biz + did•z + u;
this is a general version of a model with an interaction between a dummy variable and a quantitative
variable. [An example is in equation (7.17).]
(i) Because it changes nothing important, set the error to zero, u = 0. Then, when d = 0 we
can write the relationship between y and z as the function fo(z) = Bo + Biz. Write the same
relationship when d = 1, where you should use fi(z) on the left-hand side to denote the linear
function of z.
(ii) Assuming that & + 0 (which means the two lines are not parallel), show that the value of z*
such that fo(z*) = fi(z*) is z* = -dg/ô1. This is the point at which the two lines intersect [as
in Figure 7.2 (b)]. Argue that z* is positive if and only if 8o and &, have opposite signs.
(iii) Using the data in TWOYEAR, the following equation can be estimated:
log(wage) = 2.289 – .357 female + .50 totcoll + .030 female · totcoll
(.005)
(0.011) (.015)
n = 6,763, R² = .202,
(.003)
where all coefficients and standard errors have been rounded to three decimal places. Using this
equation, find the value of totcoll such that the predicted values of log(wage) are the same for
men and women.
(iv) Based on the equation in part (iii), can women realistically get enough years of college so that
their earnings catch up to those of men? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e2a76e8-39a2-41b2-9c0a-279511c55c09%2Fca175497-37c6-4686-8e40-6d75274c3174%2Fuysgsp.png&w=3840&q=75)
Transcribed Image Text:Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model
y = Bo + dod + Biz + did•z + u;
this is a general version of a model with an interaction between a dummy variable and a quantitative
variable. [An example is in equation (7.17).]
(i) Because it changes nothing important, set the error to zero, u = 0. Then, when d = 0 we
can write the relationship between y and z as the function fo(z) = Bo + Biz. Write the same
relationship when d = 1, where you should use fi(z) on the left-hand side to denote the linear
function of z.
(ii) Assuming that & + 0 (which means the two lines are not parallel), show that the value of z*
such that fo(z*) = fi(z*) is z* = -dg/ô1. This is the point at which the two lines intersect [as
in Figure 7.2 (b)]. Argue that z* is positive if and only if 8o and &, have opposite signs.
(iii) Using the data in TWOYEAR, the following equation can be estimated:
log(wage) = 2.289 – .357 female + .50 totcoll + .030 female · totcoll
(.005)
(0.011) (.015)
n = 6,763, R² = .202,
(.003)
where all coefficients and standard errors have been rounded to three decimal places. Using this
equation, find the value of totcoll such that the predicted values of log(wage) are the same for
men and women.
(iv) Based on the equation in part (iii), can women realistically get enough years of college so that
their earnings catch up to those of men? Explain.
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