Question 4 interested in assessing the impacts of environmental and genetic fact

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Question 4 interested in assessing the impacts of environmental and genetic factors on patients's lung function, which is measured by volume of air expelled in 1 second in liters (FEV) The potential predictors include age, sex, gene variation and smoking status. The coding sheet for these variables are as follows: In a study for 300 respiratory disease patients, the investigators were me ariable FEV Age Sex Gene variation Smoking orced expiratory volume n litersn Subjects age, in years 0-Female, 1-Male 0 = no gene variation, 1 = presence of gene variation 0=non-smoking, I-light smoking, 2=heavy smoking First, we fit main effect model with all the n 300 observations, using age, sex, gene variation and smoking status as predictors: +84 1(Smoking, = 1) +Al(Smoking, = 2) +En i=1,2, , n, (1) where I(Smoking-1) and I(Smoking,2 are indicators for light and heavy smoking respectively, with non-smoking as the reference level. We obtain the following SAS out- put for model 1). A few items have been removed and replaced by clusters of x's. The REG Procedure: Model (1) Dependent Variable: FEV Number of Observations Used 300 Analysis of Variance DF Sum of Squares Mean Square F Value Prob F .0001 Model Error Total 97.02 0.37369 299 291. 13370 le size n=300 n° 0.6226 rogression paraneter ostimatos -0.063 , 2=0.673,=-0.366 , 4=0.419, 5=-0.967 Complete the 5 missing numbers in the Analysis of Variance Table Interpret the regression parameter estimates for Age and heavy smoking, ectively Then, we fit a multiple linear regression model by adding interactions bet ween smoking levels and gene variation into interactios "model (2)". We obtain the following SAS output for modl 2). A few n model 1). We call this regression model with items have been removed from the SAS output and replaced by clusters of x's. The REG Procedure: Model (2) Dependent Variable: FEV Number of Observations Used 300 Analysis of Variance Source Model Error Total DF Sm of SquaresMean Square F Value ProbF XXXx 72.16 .0001 106. 64543 Xxxx 299 291.13370 Write out the expression for regression model (2)?

Explanation / Answer

(first part)

first we find the df of model as there are total 6 regression coefficient so df for model=6-1=5

error df=total df- model df=299-5=294

we find the SS(error)=MS(erro)*df (error)=0.37369*294=109.8649

model SS=total SS-error SS=291.1337-109.8649=181.2688

model MS=model SS/model df=181.2688/5=36.2538

FEV will increase with inrease in age as its coefficient is positive

FEV will decrease with heavy smoking

(third part)

here model df will be 8-1=7 as there will be two interaction term in addition of model 1 ( in which there are 6 regression coefficient)

source df SS MS F P model 5 181.2688 36.25377 97.01562 <0.001 error 294 109.8649 0.37369 total 299 291.1337

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