$5)$ The diabetes data set is a prospective study of onset of adult diabetes given a number of risk factors among the Pima Indian tribe. Using the diabetes.csv data set $(100)$

a$.$ Separate the first half of the data from the second half, use the first half for training, second for testing

b$.$ Using the training data

i$.$ Construct the full logistic regression model for outcome

ii$.$ Using backwards selection construct the logistic regression model with every p value for the coefficients Show Steps!!!$)$

c$.$ Predict the "response" $($eg type$=$"response"$)$ for the full logistic regression model for

i$.$ the training data set,

ii$.$ the test data set, d$.$ Predict the "response" for the smallest logistic model from the backwards selection exercise

i$.$ the training data set,

ii$.$ the test data set,

e$.$ Using random forest, build a model on the training data

f$.$ You now have $3$ models, Full Logistic, smallest logistic, and random forest. For predictions of each calculate and tabulate

i$.$ Number of correct positives

ii$.$ Number of False positives

iii. Number of correct negatives

iv$.$ Number of false negatives. g$.$ Using the results of $\backslash ($ f $\backslash ),$ is there one of the $3$ methods which appears best in modeling new results, or does it depend on whether it is more important to identify positives $($predict diabetes$)$ or negatives $($predict health$)$

h$.$ Now redo analysis twice using random selection of $384$ out of $768$ for training and the complement for testing. Is there anything you can conclude with this additional information about the merits of each approach?