Question

PART Two: SIMPLE LINEAR REGRESSION Transient hypothyroxinemia, a common finding in premature infants, is not thought to have long-term consequences or to require treatment. We conduct a study to investigate whether hypothyroxinemia in premature infants is a cause of subsequent motor and cognitive abnormalities. Blood thyroxine values were obtained on routine screening in the first week of life from 536 infants who weighed 2000 g or less at birth and were born at 33 weeks gestation or earlier. The data in below Table is presented concerning the relationship between mean thyroxine level and gestational age. Gestational age Mean thyroxine level (mg/dl) < 24 6.5 25 7.1 26 7.0 27 7.1 28 7.2 29 7.1 30 8.1 31 8.7 32 9.5 33 10.1 a treated as 24 in subsequent analyses Suppose we want to test the null hypothesis that there is not a linear relationship between gestational age (x gest) and mean thyroxine level (y. thyro). We analyze the data using SAS's REG procedure and observe the results shown in Table 2 (see page 6). Based on those findings, answer the following questions. Using the regression equation (Y = a + bx), calculate the predicted mean thyroxine level when gestational age is 34 weeks?

Answer 1

X Values 24 25 10.1 - Y Values 6.5 7.1 7.0 7.1 7.2 7.1 8.1 8.7 9.5 10.1 D 9.1 - Y.Dependent 33 8.1 - M: 28.5 M: 7.84 7.1- . 6.11 24 27 33 1 36 30 X-Independent Regression Line (9 -0.37% -2.63) Estimated y Estimate 34 9.86 Calculation Summary Sum of X= 285 Sum of Y = 78.4 Mean X = 28.5 Mean Y = 7.84 Sum of squares (55%) = 82.5 Sum of products (SP) = 30.3 Regression Equation = ý = bx + a b = SPISSx = 30.3/82.5 = 0.36727 a = My-bMx = 7.84 - (0.37*28.5) = -2.62727 9 = 0.36727X - 2.62727 X-Mx Y - My -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 -1.34 -0.74 -0.84 -0.74 -0.64 -0.74 0.26 0.86 1.66 2.26 (X-MX) 20.25 12.25 6.25 2.25 0.25 0.25 2.25 6.25 12.25 20.25 (X-MX/Y - My) 6.03 2.59 2.1 1.11 0.32 -0.37 0.39 2.15 5.81 10.17 SS: 82.5 SP: 30.3

Sol:- Linear Regression equation y = 0.36727 2 - 2.62727 x=34 Estimated tý) = 0.36727(3+) – 2062727 =9.85991 ~9.86
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