In this assignment, we are trying to predict final grades of students using their grades from homeworks and

midterm. Each of you will work with slightly different data. Here is the data we have $($from last year's Math $104$

course$).$

Which data you will use: Consider the last digit of your student number, let's call it d$.$ Use the data of $10$ students

belonging to Student $d$ to Student d$+9.$ For example, if your student id ends with $3$ use the data between Student

$3$ and Student $12.$ If it ends with $0$ use students $10$ through $19.$

What to submit: Submit a pdf file including your solutions and explanations. You can use jupyter notebook file

or a document preparation software such as Word etc., or even you can use your handwriting. For the

calculations use python and add the code you run into your homework as well.

First attempt: We are trying to predict final grades using only homework grades with a regression

equation in the form: $f^{?}=c_{1}HW+c_2$

Find $c1$ and c$2$ using pseudoinverse. Create matrix A $(10$x$2),$ then find the pseudoinverse of A and

multiply it with the known final grades to find $c1$ and $c2$ values. At the end find the RMS error

between the real and predicted final grades using the $c1$ and $c2$ values for the $10$ students that you

work with.

Second attempt: This time use midterm grades to predict final grades. Repeat all steps from part $1$

replacing homework grades with midterm grades.

Third attempt: Here, you will use both homework and midterm grades to predict the final grades. Our

equation is in form: $f^{?}=c_{1}HW+c_{2}MT+c_3$

Repeat the steps again. This time A will be a $10$ by $3$ matrix.

Compare the three cases. Which attempt gave the best predictions, which was the worst? Discuss the

results.