Question
1. a) Fit a logistic regression model to the attached low birth weight data (data are in the .dat file and variable explanations are in .txt file), using the binary outcome of variable 8 for low birth weight, with the following predictors: variables 3, 5, and 6, i.e. the smoking status, age and weight of mother. Find the best model using these predictors by removing the predictors that are not significant.
b) Repeat a) using the probit link and the cloglog link functions.
c) Compare the AIC and BIC of different models in a table and choose the best model.
d) Based on the best model, calculate the odds and the probability of a mother to give a low birth weight if she is 30 years old smoker with a body weight of 120 pounds.

2. a) Using the same data set but variable 7 birthweight (BWT) as the response variable. Fit a linear model with the same three predictors. Find the best model, you may need to check the residual plot to decide if you need a transformation of the response variable. Choose the best model. b) Compare your best model with the model you have in fitting the binary data. Do those significant parameters remain the same in the two models? Do they have the same sign of effect in the two model settings? c) For the same mother of 30 years old smoker with a body weight of 120 pounds, will she deliver a low birth weight baby based on this linear model and the cut-off birth weight of 2500 gram?
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library(dplyr)
library(caret)
library(MASS)

# Reading data
dat <- read.table("data.dat")

# Fitting logistic regression using 3, 5 and 6.
fit_3_5_6 <- glm(V8 ~ V3+V5+V6, data = dat)
fit_3_5_6$coefficients
# Coefficient of 6 is almost 0, removing 6
fit_3_5 <- glm(V8 ~ V3+V5, data = dat)
fit_3_5$coefficients

# Coefficient of 5 is almost 0, removing 5
fit_3 <- glm(V8 ~ V3, data = dat)

# Preparing table having model information AIC and BIC values
model1 <- list(Model = "3_5_6", AIC = fit_3_5_6$aic, BIC = BIC(fit_3_5_6))
model2 <- list(Model = "3_5", AIC = fit_3_5$aic, BIC = BIC(fit_3_5))
model3 <- list(Model = "3", AIC = fit_3$aic, BIC = BIC(fit_3))
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        Backtrace
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        3.08mstwenty4_siteHomeworkLibraryController.php#97
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        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        Backtrace
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      • select * from `subjects` where `subjects`.`id` in (299)
        1.03mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 37407 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.25mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
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        Backtrace
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