1. Geriatrics researcher studied the effects of two interventions on the frequency of falls. Subjects were at least 65 years of age and in reasonably good health. The variables found in the dataset geriatric.txt are: number of falls, intervention (0=education, 1=education and aerobics), sex (0=female), balance index, strength index.
(a) Fit a Poisson regression model (without overdispersion) µ = exp(β0 + β1x1 + β2x2 + β3x3 + β4x4) where:
x1 = intervention, x2 = sex, x3 = balance index, x4 = strength index.
State the estimated coefficients, their estimated standard errors, and the estimated re- sponse function.
(b) Obtain the model deviance and perform a goodness-of-fit test. State your conclusion.
(c) Plot the deviance residuals (versus their index). Do there appear to be any outlying cases?
(d) Use both AIC and deviance test to test the hypothesis that sex can be dropped from the model. What is your conclusion?
(e) Fit the model without X2. Obtain an approximate 95% confidence interval for β1 and interpret the confidence interval.
(f) Does aerobic exercise reduce the frequency of falls when controlling for balance and strength?

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Part a)
R Code is given below:
geriatric = read.table("C:/Users/GCE Employee/Downloads/geriatric.txt", header= TRUE) # read text file
attach (geriatric)
#install required packages
install.packages ("ggplot2")
install.packages ("sandwich")
install.packages ("msm")
#poisson regression
summary(m1 <- glm(Fall ~ Int + Sex+BI+SI, family="poisson", data=geriatric))

R Output is given below:
glm(formula = Fall ~ Int + Sex + BI + SI, family = "poisson",
    data = geriatric)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-2.1854 -0.7819 -0.2564   0.5449   2.3626

             Estimate Std. Error z value Pr(>|z|)   
(Intercept) 0.489467   0.336869   1.453 0.14623   
Int         -1.069403   0.133154 -8.031 9.64e-16 ***
Sex         -0.046606   0.119970 -0.388 0.69766   
BI          0.009470   0.002953   3.207 0.00134 **
SI          0.008566   0.004312   1.986 0.04698 *

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