How can I Use R code to solve this

$.$ The Mailing Experiment

Tayko$$has supplied its customer list of $200,000$ names to the pool, which totals over $5$ million names, so it is now entitled to draw $200,000$ names for a mailing.$$Tayko$$would like to select the names that have the best chance of performing well, so it first conducts a$$test prior to withdrawing its full allotment of names $$ it$$draws $20,000$ names from the pool and does a test mailing of the new catalog.

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This mailing yielded $1,065$ purchasers, a response rate of $0\mathrm{.}053,$ or $5\mathrm{.}3\%.$ To optimize the performance of the data mining techniques, it was decided to work with a stratified sample that contained equal numbers of purchasers and$$nonpurchasers$.$ For ease of presentation, the dataset for this case includes just $1,000$ purchasers and $1,000$nonpurchasers$,$ an apparent response rate of $0\mathrm{.}5,$ or $50\%.$ Therefore, after using the dataset to predict who will be a purchaser, we must adjust the purchase rate back down by multiplying each case's $$probability of purchase$$ by $0\mathrm{.}053/0\mathrm{.}5,$ or $0\mathrm{.}107.$

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Data

There are two response variables in this case.$$Purchase indicates whether or not a prospect responded to the test mailing and purchased something.$$Spending$$indicates$,$ for those who made a purchase, how much they spent.

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The overall procedure in this case will be to develop two models. The first model will be used to classify records as Purchase or No purchase. This model will be used to identify the most likely purchasers in the consortium$$s database.$$ The second model will be used for those cases that are classified as having made a purchase$$and will predict the amount purchasers spend.$$ By identifying the most likely responders and the highest spenders Tayko hopes to identify names from the consortium$$s pool that will increase profit above a random draw of names.

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Table $21\mathrm{.}7$ in the textbook provides a description of the variables in the Tayko dataset.

A catalog costs $$2$ to mail, has response rate of $0\mathrm{.}053$ or $5\mathrm{.}3\%,$ and the average spend you can determine based on purchasers in a test database. How do I estimate the gross profit that a company could expect from the remaining names if selected them randomly from the pool, using R Studio?

Assignment Details

$1.$ Each catalog costs $$2$ to mail $($including printing, postage, and mailing costs$).$

a$.$ Based on this cost, the response rate from the test, and the average spend you can determine based on the purchasers in the dataset, estimate the gross profit that the firm could expect from the remaining $180,000$ names if it selected them randomly from the pool.$$

$2.$ The first model you will develop is a model for classifying a customer as a purchaser or$$nonpurchaser$.$ This will identify the most likely responders to a mailing.

a$.$ Partition the data randomly into a training set $(800$ records$),$validation set $(700$ records$),$ and$$test set $(500$ records$).$

b$.$Run a logistic regression model on the training set using backward elimination to select the best subset of variables.$$ Exclude Spending as it is a dependent variable.$$

c$.$ Assess your model results by using confusion matrices for the training and validation data, and the decile lift chart on the validation data.$$ Do you feel this is an adequate model to move forward? Support your assessment with specific accuracy and lift information.

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$3.$ The second model you will develop is a model for predicting spending among the purchasers.$$ This will identify the highest spenders.

a$.$ Create a vector of IDs for only the purchaser records $($Purchase $=1).$

b$.$ Partition this dataset into the training and validations records. $($Use the same training$/$validation labels from the earlier partitioning; one way is to use function intersect$()$ to find IDs of purchasers in the original partitions$).$

c$.$Develop models for predicting spending, using:

i$.$Multiple linear regression using backward selection

ii$.$Regression trees $($with default parameters which will prune tree$)$

d$.$ Choose one model on the basis of its performance on the validation data.$$ What is

$$ your rationale for choosing the model you chose?

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