Homework SourseDataset here httppeoplestatsfucalwa68teachingStat305lowbwttx
Dataset here: http://people.stat.sfu.ca/~lwa68/teaching/Stat305/lowbwt.txt
The data set lowbwt also contains sex, a dichotomous random variable designating the gender of each infant.
(a) (2 marks) Add the indicator variable sex – where 1 represents a male and 0 a female –to the model that contains gestational age. Given two infants with identical gestational ages, one male and the other female, which would tend to have the higher systolic blood pressure? By how much, on average?
(b) (2 marks) Add to the model a third explanatory variable that is the interaction between gestational age and sex. Does gestational age have a different effect on systolic blood pressure depending on the gender of the infant?
Solution
(a) (2 marks) Add the indicator variable sex – where 1 represents a male and 0 a female –to the model that contains gestational age. Given two infants with identical gestational ages, one male and the other female, which would tend to have the higher systolic blood pressure? By how much, on average?
Since male represents 1 in sex variable, males tend to have the higher systolic blood pressure by 1.3563 on average.
Regression Analysis
R²
0.082
Adjusted R²
0.064
n
100
R
0.287
k
2
Std. Error
11.035
Dep. Var.
sbp
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,061.7346
2
530.8673
4.36
.0154
Residual
11,811.6254
97
121.7693
Total
12,873.3600
99
Regression output
confidence interval
variables
coefficients
std. error
t (df=97)
p-value
95% lower
95% upper
Intercept
10.0071
12.7227
0.787
.4335
-15.2441
35.2582
sex
1.3563
2.2231
0.610
.5432
-3.0559
5.7685
gestage
1.2626
0.4376
2.885
.0048
0.3940
2.1312
(b) (2 marks) Add to the model a third explanatory variable that is the interaction between gestational age and sex. Does gestational age have a different effect on systolic blood pressure depending on the gender of the infant?
Gestational age does not have a different effect on systolic blood pressure depending on the gender of the infant because interaction between age and gender is not significant ,t=0.597, P=0.5518.
Regression Analysis
R²
0.086
Adjusted R²
0.057
n
100
R
0.293
k
3
Std. Error
11.072
Dep. Var.
sbp
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,105.4463
3
368.4821
3.01
.0341
Residual
11,767.9137
96
122.5824
Total
12,873.3600
99
Regression output
confidence interval
variables
coefficients
std. error
t (df=96)
p-value
95% lower
95% upper
Intercept
14.9805
15.2419
0.983
.3282
-15.2744
45.2355
sex
-15.1570
27.7433
-0.546
.5861
-70.2270
39.9130
gestage
1.0903
0.5254
2.075
.0406
0.0475
2.1332
sex.age
0.5714
0.9569
0.597
.5518
-1.3280
2.4709
| Regression Analysis | ||||||
| R² | 0.082 | |||||
| Adjusted R² | 0.064 | n | 100 | |||
| R | 0.287 | k | 2 | |||
| Std. Error | 11.035 | Dep. Var. | sbp | |||
| ANOVA table | ||||||
| Source | SS | df | MS | F | p-value | |
| Regression | 1,061.7346 | 2 | 530.8673 | 4.36 | .0154 | |
| Residual | 11,811.6254 | 97 | 121.7693 | |||
| Total | 12,873.3600 | 99 | ||||
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=97) | p-value | 95% lower | 95% upper |
| Intercept | 10.0071 | 12.7227 | 0.787 | .4335 | -15.2441 | 35.2582 |
| sex | 1.3563 | 2.2231 | 0.610 | .5432 | -3.0559 | 5.7685 |
| gestage | 1.2626 | 0.4376 | 2.885 | .0048 | 0.3940 | 2.1312 |
