1. Eva Ørnbøl + Morten Frydenberg
Homework: 1.1
Sunday, 21 April 2019
graph box scl, over(bmi_who)
Linear and Logistic Regression: Homework

2. Eva Ørnbøl + Morten Frydenberg
Homework: 1.1
Sunday, 21 April 2019
hist scl, by(bmi_who)
Linear and Logistic Regression: Homework

3. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.2
xi: regress scl sbp i.sex i.bmi_who
i.bmi_who _Ibmi_who_ (naturally coded; _Ibmi_who_0 omitted)
i.sex _Isex_ (naturally coded; _Isex_1 omitted)
Source | SS df MS Number of obs =
F( 5, 4652) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp |
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_2 |
_cons |
Linear and Logistic Regression: Homework

4. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.3
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp |
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_2 |
_cons |
sbp: the expected difference in scl between two persons of the same gender and in the same bmi group who differ one unit of sbp.
sbp: the expected difference in scl between two persons who differ one unit of sbp, “adjusted” for gender and bmi group in a model without interaction.
Linear and Logistic Regression: Homework

5. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.3
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp |
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_2 |
_cons |
_Ibmi_who_3: the expected difference in scl between a obese (BMI>30 kg/m2) person and a underweight person, “adjusted” for gender and blood pressure.
Linear and Logistic Regression: Homework

6. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.3
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp |
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_2 |
_cons |
_Isex_2: the expected difference in scl between a woman and a man “adjusted” for blood pressure and bmi group.
Linear and Logistic Regression: Homework

7. Eva Ørnbøl + Morten Frydenberg
Homework: 1.3
Sunday, 21 April 2019
Linear and Logistic Regression: Homework

8. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.4
gen sbp85=sbp-85
char sex [omit]2
char bmi_who [omit]1
xi: regress scl sbp85 i.sex i.bmi_who
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp_85 |
_Ibmi_who_0 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_1 |
_cons |
The expected value of a woman in bmi group 1 with sbp of 85 is: (204.3 ; 210.7) .
Linear and Logistic Regression: Homework

9. Homework: 1.5 -----------------------------------------------------
Variable | model model 1 model 3
sbp | |
dbp | |
_Ibmi_who_1 | |
_Ibmi_who_2 | |
_Ibmi_who_3 | |
_Isex_2 | |
_cons | |
N |
df_r |
F |
rss |
legend: b/se

10. Homework: 1.5

11. xi: regress scl sbp sbp2 i.sex i.bmi_who
Homework: 1.6
gen sbp2=sbp^2
xi: regress scl sbp sbp2 i.sex i.bmi_who
i.bmi_who _Ibmi_who_ (naturally coded; _Ibmi_who_0 omitted)
i.sex _Isex_ (naturally coded; _Isex_1 omitted)
Source | SS df MS Number of obs =
F( 6, 4651) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp |
sbp2 |
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_2 |
_cons |

12. Homework: 1.6

13. Eva Ørnbøl + Morten Frydenberg
Sunday, 21 April 2019
Homework: 1.6
gen sbp85=sbp-85
gen sbp285=sbp85^2
char sex [omit]2
char bmi_who [omit]1
xi: regress scl sbp85 sbp285 i.sex i.bmi_who
scl | Coef. Std. Err t P>|t| [95% Conf. Interval]
sbp_85 |
sbp2_85 |
_Ibmi_who_0 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_Isex_1 |
_cons |
The expected value of a woman in bmi group 1 with sbp of 85 is: (189.7 ; ).
Compared to the result from model 1: (204.3 ; 210.7)
Linear and Logistic Regression: Homework

14. Homework: 1.7 ----------------------------------------
Variable | Model Model 1
sbp | |
bmi | |
_Isex_2 | |
_Ibmi_who_1 | |
_Ibmi_who_2 | |
_Ibmi_who_3 | |
_cons | |
N |
df_r |
F |
rss |
legend: b/se

15. Homework: 1.7

16. Homework: 1.8
Original scl: residuals in bmi group for both genders.

17. Homework: 1.8
Original scl:

18. Homework: 1.8
Original scl:

19. Homework: 1.8
Ln transformed scl: residuals in bmi group for both genders.

20. Homework: 1.8
Ln transformed scl:

21. Homework: 1.8
Ln transformed scl:

22. xi: regress lnscl i.sex*sbp_85 i.sex*i.bmi_who
Homework: 1.9
gen lnscl=ln(scl)
xi: regress lnscl i.sex*sbp_85 i.sex*i.bmi_who
i.sex _Isex_ (naturally coded; _Isex_1 omitted)
i.sex*sbp _IsexXsbp_# (coded as above)
i.bmi_who _Ibmi_who_ (naturally coded; _Ibmi_who_0 omitted)
i.sex*i.bmi_who _IsexXbmi_#_# (coded as above)
Output omitted
lnscl | Coef. Std. Err t P>|t| [95% Conf. Interval]
_Isex_2 |
sbp_85 |
_IsexXsbp_~2 |
_Isex_2 | (dropped)
_Ibmi_who_1 |
_Ibmi_who_2 |
_Ibmi_who_3 |
_IsexXbmi_~1 |
_IsexXbmi_~2 |
_IsexXbmi_~3 |
_cons |

23. Homework: 1.10
The interaction _IsexXsbp_1_2 is the difference in coefficient to sbp_85 between the women and men.
Lets consider the first BMI group (BMI on reference level):
For men the line is as follows:
logscl= *(sbp-85)
For women the line is as follows:
logscl=( )+( )*(sbp-85)

24. Homework: 1.10
The interaction _IsexXsbp_1_2 is the difference in coefficient to sbp_85 between the women and men.
Lets consider the second BMI group :
For men the line is as follows:
logscl=( ) *(sbp-85)
For women the line is as follows:
logscl=( )
+( )*(sbp-85)

25. Homework: 1.11
The interaction coefficient _IsexXbmi_2_2 is the extra difference in level between overweight men and women compared to underweight men and women.
testparm _IsexXbmi_*
( 1) _IsexXbmi_2_1 = 0
( 2) _IsexXbmi_2_2 = 0
( 3) _IsexXbmi_2_3 = 0
F( 3, 4648) =
Prob > F =

26. Homework: 1.11
Lets consider the first bmi group:
For men the level is as follows:
logscl=5.28
For women the level is as follows:
logscl=
Then we look at the second bmi group:
logscl=
logscl=( )+( )

27. Homework: 1.7

28. Homework: 1.7