hw10sol.2 - STA 6934 7) CHAPTER #19 Variable Diet Group...

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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 n-q-1= 100-4-1 = 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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