1- 4. A study was performed to investigate whether hypothyroxinemia in premature
ID: 3315962 • Letter: 1
Question
1- 4. A study was performed to investigate whether hypothyroxinemia in premature infants is a cause of subsequent motor and cognitive abnormalities. Blood thyroxine values were obtained and their mean (vi) for each gestational age (GA) (x) were obtained in the first week of life from infants who weighed 2000 grams or less at birth and were born at 33 weeks gestation or earlier. The data were then summarized into 10 gestational ages and corresponding mean thyroxine values. The following quantities are given for this study. GA (xi) Mean thyroxine (y) 6.5 7.1 7.0 7.1 7.2 7.1 8.1 8.7 9.5 10.1 24 25 26 27 28 29 30 31 32 33 10 10 10 10 10 x, -285, x2-8205, yi =78.4, Y =627.88, x), = 2264.7 i-1 i-1 i-1 i-1 i=1 1. What is the best statistical model to study how the mean thyroxine value depends on the gestational age? Write out the model 2. How do you estimate the parameters of the model? Calculate the model parameters 3. What value will you predict for a mean gestational age of 35 weeks if the model is valid? 4. How do you interpret the model you estimated?Explanation / Answer
From Excel
a) dependent variable is Mean Thyroxine
Independent varaible is GA
from Excel, The correlation between two varaibles is 0.917
Hence there is 92% correlation between two varaibles.
b) The regression model is
y=a+bx
from Excel
y=-2.63+0.37*GA
c)The fitted model is
y= -2.63+0.37*GA
when GA=35
y=-2.63+0.37*GA=-2.63+0.37*35=10.32
4)
slope is 0.37
if we change one unit in GA then there is 0.37 units increase in y.
and R square=84%
That is 84% of variation in x is explained by the regression model.
SUMMARY OUTPUT Regression Statistics Multiple R 0.917348 R Square 0.841528 Adjusted R Square 0.821719 Standard Error 0.511815 Observations 10 ANOVA df SS MS F Significance F Regression 1 11.12836 11.12836 42.48204 0.000185 Residual 8 2.095636 0.261955 Total 9 13.224 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -2.62727 1.614081 -1.62772 0.142235 -6.34935 1.094804 -6.34935 1.094804 GA 0.367273 0.056349 6.517825 0.000185 0.237332 0.497214 0.237332 0.497214Related Questions
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