ECP 3004: Python for Business Analytics

Department of Economics

College of Business

University of Central Florida

Spring 2021

Assignment 5

Due Sunday, February 28, 2021 at 11:59 PM

in your GitHub repository

Instructions:

      Complete this assignment within the space on your private GitHub repo (not a fork of the course repo ECP3004S21!) in a folder called assignment 05. In this folder, save your answers to Questions 1 and 2 in a file called my A5 module.py, following the sample script in the folder assignment 05 in the course repository. When you are finished, submit it by uploading your files to your GitHub repo using any one of the approaches outlined in Question 3. You are free to discuss your approach to each question with your classmates but you must upload your own work.

Question 1:

      Follow the function design recipe to define functions for all of the following Exercises. For each function, create three examples to test your functions. Record the definitions in the sample script my_A5_module.py.

      Together, the function definitions will form a module called my_A5_module that you can read in and test using the script my_A5_tests.py. There are no particular requirements for my_A5_tests.py but you can use it to conduct any calculations or tests of your module. That way, you will not have any unnecessary commands in your module in my_A5_module.py, except for the function definitions.

Exercise 1 Write a function variance(x) that calculates the sample variance of the variable in the list x. The formula for the variance is

where n is the number of items in the list x and ¯x is the average of x.

Exercise 2 Write a function covariance(y, x) that calculates the sample covariance of the variables in the lists y and x. The formula for the covariance is

where the lists y and x both have length n.

Exercise 3 Now write a function that calculates the slope coefficients for the linear regression model. Using calculus, you can show that the following function minimizes SSR(y, x, , ) for :

which is called the ordinary least squares (OLS) estimator. Write a function that performs this calculation called ols_slope(y, x).

Exercise 4 Now write a function ols intercept(y, x, beta_1_hat) that calculates the intercept co-efficient for the linear regression model. With the slope coefficient, the intercept can be calculated with

Exercise 5 Write a function ssr(y, x, beta 0, beta_1) that calculates the sum of squared residuals for the linear regression model.

You can use the function ssr_loops(y, x, beta_0, beta_1) from Assignment 4 (including the solutions) as a template.

Exercise 6 Now find values of beta_0 and beta_1 that minimize ssr(y, x, beta_0, beta_1) for given x and y. Write a function min_ssr(y, x, beta_0_min, beta_0_max, beta 1 min, beta_1_max, step) as follows:

a) Find these values by evaluating ssr(y, x, beta 0, beta 1) over every combination of of (, ) in two lists.

b) Create lists beta 0 list and beta_1_list from ranges = , . . . ,  and = , . . . , , where the neighboring values of or are separated by distance step.

c) Start with min SSR = 999999. Loop over the index numbers i and j, corresponding to lists beta 0 list and beta 1 list.

d) For each pair of i and j, extract the value beta_0_list[i] and beta_1_list[j].

e) For each pair of i and j, evaluate SSR(y, x, , ). If it is lower than min_SSR, record the new i_min = i and j_min = j and update the newest value of min_SSR.

f) After the loops, return [ beta_0[i_min], beta_1[j_min] ]

g) Verify that the result matches the values in Exercises 4 and 5 (up to accuracy step).

Question 2:

      For all of the Exercises in Question 1, use your examples to test the functions you defined. Since the examples are all contained within the docstrings of your functions, you can use the doctest.testmod() function within the doctest module to test your functions automatically. To conduct any tests, use the sample program my_A5_tests.py, run the lines of code, and make any corrections, as necessary.

      Don’t worry about false alarms: if there are some “failures” that are only different in the smaller decimal places, then your function is good enough. It is much more important that your function runs without throwing an error.

Question 3:

      Push your completed files to your GitHub repository following one of these three methods.

Method 1: In a Browser

1. Browse to your assignment 0X folder in your repository (“X” corresponds to Assignment X.).

2. Click on the “Add file” button and select “Upload files” from the drop-down menu.

3. Revise the generic message “Added files via upload” to leave a more specific message. You can also add a description of what you are uploading in the field marked “Add an optional extended description...”

4. Press “‘Commit changes,” leaving the button set to “Commit directly to the main branch.”

Method 2: With GitHub Desktop

1. Save your file within the folder in your repository in GitHub Desktop.

2. When you see the changes in GitHub Desktop, add a description of the changes you are making in the bottom left panel.

3. Press the button “Commit to main” to commit those changes.

4. Press the button “Push origin” to push the changes to the online repository. After this step, the changes should be visible on a browser, after refreshing the page.

Method 3: At the Command Line

1. Open GitBash or Terminal and navigate to the folder inside your local copy of your git repo containing your assignments. Any easy way to do this is to right-click and open GitBash within the folder in Explorer. A better way is to navigate with UNIX commands, such as cd.

2. Enter git add . to stage all of your files to commit to your repo. You can enter git add my_filename.ext to add files one at a time, such as my_functions.py in this Assignment.

3. Enter git commit -m "Describe your changes here", with an appropriate description, to commit the changes. This packages all the added changes into a single unit and stages them to push to your online repo.

4. Enter git push origin main to push the changes to the online repository. After this step, the changes should be visible on a browser, after refreshing the page.