Modify the code in the file Gradient descent and logistic regression.R which

is located on our canvas page to do the following. Do not use glm or any

similar function.

$($a$)$ Using the iris dataset, already in R$,$ create a new data frame consist$-$

ing of just the first $100$ data points. This data will include only two

types of flowers: setosa and versicolour.

$($b$)$ Randomly select $30$ flowers from each of the two types to be your

training set and the remainder to be your testing set.

$($c$)$ Train a logistic model on your training data

$($d$)$ predict the flower type using the testing data and construct a con$-$

fusion matrix. How accurate was your model on the training and

testing data?

$($e$)$ Now, Load the file numbers.csv into memory. This dataset consists

of $42,000$ hand drawn digits $(0$ through $9).$ Each row of data is a

digit.

$($f$)$ The first column of the dataset lets you know what the digit is sup$-$

posed to be$.$ create a variable y$,$ a $42000$ length vector, that takes

the value $0$ if the digit is even and $1$ if the digit is odd.

$($g$)$ Set the seed to $1$ and shuffle the rows of the dataset. Split the data so

that our training data is the first $10,000$ digits and the testing data

is the remainder of the data.

$($h$)$ Use your modified code to train a logistic regression model on the

training data and then test the accuracy of the model on the training

data. This could take a long time if your code is not efficient or if

the number of epochs you do it large.

$($i$)$ Use you newly found logistic model to predict the digits on the testing

data. Construct a confusion matrix and note the accuracy of your

model. $($Note that a logistic regression model is not the best way to

classify images. If you take a course in machine learning then you

would probably see Convolutional Neural Networks which is a more

powerful technique for classifying images.$)$