Unformatted text preview: STA 6934 7) CHAPTER #19
Variable
Diet Group
Base line Cholesterol
Body Mass Index
Gender Coefficient
11.25
0.85
0.23
3.02 Standard Error
4.33
0.07
0.65
4.42 a) Null Hypothesis: Ho : Bi=0 Where i=1, 2, 3, 4 ( for four different groups)
t = B1 – Bi0
Assuming N=100, we have nq1= 10041 = 95 Df
Se (B1)
Diet Group:
t = 11.25 / 4.33
= 2.598
For 95 df, p value <0.05 We reject the Null and conclude that Diet
group has significant effect on Cholesterol
Base line Cholesterol t = 0.855/0.07
= 12.143
For 95 df, p value <0.001 We reject the Null and conclude that Base
line Cholesterol group has significant effect on Cholesterol
Body Mass Index
t = 0.23/0.65
= 0.354
For 95 df, p value > 0.2 We fail to reject the Null and conclude that
BMI group does not have significant effect on Cholesterol
Gender
t= 3.02/4.42
= 0.683
For 95 df, p value >0.2 We fail to reject the Null and conclude that
Gender doesn’t have significant effect on Cholesterol
b) Since the coefficient for BMI = 0.23, having all the other explanatory variables to
be constant , if BMI is increased by 1 Kg/m2, then the serum cholesterol level
would increase by 1 * 0.23= 0.23
c) Since the coefficient for BMI = 0.23, having all the other explanatory variables to
be constant , if BMI is increased by 10 Kg/m2, then the serum cholesterol level
would increase by 10 * 0.23= 2.3
d) Y = 0.85 + 0.23 x1 – 11.25 x2 – 3.02 x3
If the indicator variable gender is coded so that male (x3 = 1) and female (x3=0),
then after 8 weeks of time, we have
Y for Males = 0.85 + 0.23 x1 – 11.25 x2 – 3.02 (1) = Total – 3.02
Y for Female = 0.85 + 0.23 x1 – 11.25 x2 – 3.02 (0) = Total
(Where Total is the value considering x1 and x2)
Thus we see that Females have higher serum cholesterol level by 3.02 than the
males.
8) a) Referring to fig. 19.8, we can conclude that there does appear a linear relationship
between Apgar score and SBP. b) Y = + 1 x1 + 2 x2 = 9.8034 + 0.4875 (x1) + 1.1848(x2)
If Apgar score is kept constant, then a 1 week increase in gestation age would yield a
0.4875 increase in SBP. In simple words, B1 indicates the increase in Blood pressure
per year of gestation age, provided that all other variables remain constant.
Similarly, if Gestation age is kept constant, increase in per point value of Apgar
would yield 1.848 increase in SBP.
c) Applying the Least Squares Regression Model, we get
Y = 9.8034 + 0.4875 (31) + 1.1848(7) = 33.21
e) Null Hypothesis: Ho : B2=0
t = Bapgar
= 1.1848/0.4424 = 2.6781
Se(B2)
For 97 df, referring the t distribution, we get, p value < 0.001. Hence we can
reject the Null hypothesis and conclude that the coefficient concerning the Apgar score is
not equal to 0 and therefore does impact the systolic blood pressure.
f) Magnitude of R2 = 0.08944. Previous data yielded an R2 =0.07895, an addition of
5 minute APAR resulted in slight improvement to predict systolic BP.
g) The plot indicates that homoscedasticity has not been violated and that the
standard deviation is equal across all values.
9)
b) Refer Plot. The plot has a positive correlation between Gender and SBP. The
regression lines for males and females are very similar.
c) No. The interaction is not significantly different from zero, so it appears gestation
does not have a differential effect based on gender.
d) No. The coefficients are not significant and the plots suggest very little effect of
gender on either the intercept or slope of the regression line of gestation on SBP. ...
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