1. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Multiple Regression
EPP 245
Statistical Analysis of
Laboratory Data

2. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Cystic Fibrosis Data
Cystic fibrosis lung function data
lung function data for cystic fibrosis patients (7-23 years old)
age a numeric vector. Age in years.
sex a numeric vector code. 0: male, 1:female.
height a numeric vector. Height (cm).
weight a numeric vector. Weight (kg).
bmp a numeric vector. Body mass (% of normal).
fev1 a numeric vector. Forced expiratory volume.
rv a numeric vector. Residual volume.
frc a numeric vector. Functional residual capacity.
tlc a numeric vector. Total lung capacity.
pemax a numeric vector. Maximum expiratory pressure.
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

3. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Some Stata Commands
. insheet using "cystfibr.csv"
(11 vars, 25 obs)
. graph matrix age sex height weight bmp fev1 rv frc tlc pemax
. graph export cystfibr-scm.wmf
. regress pemax age sex height weight bmp fev1 rv frc tlc
. rvfplot
. graph export cystfibr-rvf.wmf
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

4. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

5. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Source | SS df MS Number of obs =
F( 9, 15) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
sex |
height |
weight |
bmp |
fev1 |
rv |
frc |
tlc |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

6. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Source | SS df MS Number of obs =
F( 9, 15) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
sex |
height |
weight |
bmp |
fev1 |
rv |
frc |
tlc |
_cons |
T-test of additional value of variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

7. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Source | SS df MS Number of obs =
F( 9, 15) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
sex |
height |
weight |
bmp |
fev1 |
rv |
frc |
tlc |
_cons |
Test of whole model
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

8. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

9. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Source | SS df MS Number of obs =
F( 9, 15) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
sex |
height |
weight |
bmp |
fev1 |
rv |
frc |
tlc |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

10. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax age height weight bmp fev1 rv frc tlc
Source | SS df MS Number of obs =
F( 8, 16) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
height |
weight |
bmp |
fev1 |
rv |
frc |
tlc |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

11. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax age height weight bmp fev1 rv frc
Source | SS df MS Number of obs =
F( 7, 17) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
height |
weight |
bmp |
fev1 |
rv |
frc |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

12. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax age height weight bmp fev1 rv
Source | SS df MS Number of obs =
F( 6, 18) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
age |
height |
weight |
bmp |
fev1 |
rv |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

13. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax height weight bmp fev1 rv
Source | SS df MS Number of obs =
F( 5, 19) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
height |
weight |
bmp |
fev1 |
rv |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

14. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax weight bmp fev1 rv
Source | SS df MS Number of obs =
F( 4, 20) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
weight |
bmp |
fev1 |
rv |
_cons |
Least significant variable
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

15. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress pemax weight bmp fev1
Source | SS df MS Number of obs =
F( 3, 21) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
weight |
bmp |
fev1 |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

16. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. stepwise, pr(.05): regress pemax age sex height weight bmp fev1 rv frc tlc
begin with full model
p = >= removing sex
p = >= removing tlc
p = >= removing frc
p = >= removing age
p = >= removing height
p = >= removing rv
Source | SS df MS Number of obs =
F( 3, 21) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
fev1 |
weight |
bmp |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

17. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. stepwise, pr(.1) pe(.05): regress pemax age sex height weight bmp fev1 rv frc tlc
begin with full model
p = >= removing sex
p = >= removing tlc
p = >= removing frc
p = >= removing age
p = >= removing height
p = >= removing rv
Source | SS df MS Number of obs =
F( 3, 21) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
pemax | Coef. Std. Err t P>|t| [95% Conf. Interval]
fev1 |
weight |
bmp |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

18. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
Cautionary Notes
The significance levels are not necessarily believable after variable selection
The original full model F-statistic is significant, indicating that there is some significant relationship: F(9,15) = 2.93, p =
After variable selection, F(3,21) = 9.28, p = , which is biased.
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

19. EPP 245 Statistical Analysis of Laboratory Data
set obs 25
generate x1 = invnormal(uniform())
generate x2 = invnormal(uniform())
generate x3 = invnormal(uniform())
generate x4 = invnormal(uniform())
generate x5 = invnormal(uniform())
generate x6 = invnormal(uniform())
generate x7 = invnormal(uniform())
generate x8 = invnormal(uniform())
generate x9 = invnormal(uniform())
generate y = invnormal(uniform())
regress y x1 x2 x3 x4 x5 x6 x7 x8 x9
stepwise, pr(.1): regress y x1 x2 x3 x4 x5 x6 x7 x8 x9
5/25/2019
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

20. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. regress y x1 x2 x3 x4 x5 x6 x7 x8 x9
Source | SS df MS Number of obs =
F( 9, 15) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
y | Coef. Std. Err t P>|t| [95% Conf. Interval]
x1 |
x2 |
x3 |
x4 |
x5 |
x6 |
x7 |
x8 |
x9 |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data

21. EPP 245 Statistical Analysis of Laboratory Data
5/25/2019
. stepwise, pr(.1): regress y x1 x2 x3 x4 x5 x6 x7 x8 x9
begin with full model
p = >= removing x4
p = >= removing x6
p = >= removing x1
p = >= removing x7
p = >= removing x8
p = >= removing x3
p = >= removing x5
p = >= removing x9
Source | SS df MS Number of obs =
F( 1, 23) =
Model | Prob > F =
Residual | R-squared =
Adj R-squared =
Total | Root MSE =
y | Coef. Std. Err t P>|t| [95% Conf. Interval]
x2 |
_cons |
October 25, 2007
EPP 245 Statistical Analysis of Laboratory Data