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Instructor(s): Justin Eldridge

This exam was administered in-person. The exam was closed-notes, except students were allowed to bring 5 two-sided cheat sheets. No calculators were allowed. Students had 180 minutes to take this exam.

Welcome to the Final Exam for DSC 80.

This exam has several coding questions. These questions will be manually graded, and your answers are not expected to be syntactically-perfect! Be careful not to spend too much time perfecting your code.

Problem 1

In the next five questions, assume you have access to a DataFrame named pts, shown below:

Problem 1.1

What is the type of the result of the following line of code?

pts.groupby('group')['x'].max()

• int

• float

• str

• pandas.Series

• pandas.DataFrame

Problem 1.2

Suppose z is a pandas Series containing the data shown below:

>>> z
5    20
0     1
2     3
Name: z, dtype: int64

Notice that the index of this Series does not match the index of pts.

Which of the following will be the result of running:

>>> pts['z'] = z
>>> pts

Below are some of the options:

• Option 1:
• Option 2:
• Option 3:

• Option 1

• Option 2

• Option 3

• An exception will be raised because z is missing some of the rows that are in pts.

Problem 1.3

What is the result of the following code?

>>> pivot = pts.pivot_table(
    values='x',
    index='group',
    columns='color',
    aggfunc='count')
>>> pivot.loc['A', 'red']

Your answer should be in the form of a number (or possibly NaN). Your answer does NOT need to be exactly what is displayed by Python.

Problem 1.4

Suppose the costs DataFrame contains the following data:

Suppose we run:

>>> res = pts.merge(costs, how='left')

How many rows will res have?

Problem 1.5

Suppose we have defined:

def foo(ser):
    return (ser - ser.min()).max()

What will be the result of:

>>> pts.groupby('group')[['x', 'y']].aggregate(foo).loc['A', 'x']

Your answer should be in the form of a number.

Problem 2

The Earth Impact Database, curated by the University of New Brunswick’s Planetary and Space Science Centre, contains information on almost 200 impact craters caused by meteorites that have crashed into the Earth. In this question, assume you have access to a dataframe named impacts, shown below:

A short description of each column follows:

• 'crater_name': the name of the impact crater.
• 'state': if the crater is in the United States, the state containing the crater is listed here; otherwise, it is missing.
• 'country': the country containing the crater.
• 'target_rock': the type of rock that the crater is in.
• 'diameter_km': the diameter of the crater in kilometers.
• 'drilled': whether or not the crater has been drilled to analyze its contents.

Problem 2.1

There are many missing values in the state column. Upon inspection, you find that a crater is missing a state if and only if the crater is not located in the United States. Note: while we’re aware that upon inspection of the actual DataFrame, that this statement is clearly not true (such as Canada and Australia), we’ll assume that the statement is true for the sake of the problem.

What is the most likely type of the missingness in the statecolumn?

• Not Missing at Random (NMAR)

• Missing at Random (MAR)

• Missing Completely at Random (MCAR)

• Missing by Design (MD)

Problem 2.2

Suppose we want to test the following hypotheses:

• Null Hypothesis: the crater diameter of impacts in sedimentary rock comes from the same distribution as the crater diameter of impacts in mixed rock.
• Alternative Hypothesis: the crater diameter of impacts in sedimentary rock is significantly larger on average.

When the distributions of crater diameter are plotted, we see the following:

Which one of the following is the best test statistic in this case?

• Total Variation Distance (TVD) between the distributions

• Kolmogorov-Smirnov (K-S) distance between the distributions

• the signed difference between the mean crater diameter of impacts in sedimentary rock, minus the mean crater diameter of impacts in mixed rock

• the unsigned (absolute) difference between the mean crater diameter of impacts in sedimentary rock, minus the mean crater diameter of impacts in mixed rock

Problem 2.3

Suppose it is observed that some values in the column are missing. To determine if there is an association between this missingness and the values in the country column, a permutation test will be performed with the null hypothesis that the distribution of countries when the diameter is missing is the same as the distribution of countries when the diameter is not missing.

Which of the following test statistics should be used?

• the Total Variation Distance (TVD) between the distribution of countries when the diameter is missing and the distribution of countries when the diameter is not missing

• the Kolmogorov-Smirnov statistic between the distribution of countries when the diameter is missing and the distribution of countries when the diameter is not missing

• the signed difference between the mean crater diameter of impacts where the country is missing, minus the mean crater diameter of impacts where the country is not missing

• the unsigned (absolute) difference between the mean crater diameter of impacts where the country is missing, minus the mean crater diameter of impacts where the country is not missing

Problem 2.4

Suppose the permutation test described in the previous problem fails to reject the null hypothesis. Assuming that NMAR and MD have been ruled out already, what can be said about the missingness in diameter_km?

• it is MCAR

• it is MAR

• We cannot say for sure without first testing for an association between the missingness and the other columns besides country.

Problem 2.5

Suppose we fill in the missing values in the diameter_km column by random sampling. That is, for each missing diameter, we randomly sample from the the set of observed diameters. You may assume that these samples are drawn from the uniform distribution on observed diameters, and that they are independent.

Assume that it is known that the missingness in the diameter_km column is MAR. Which of the following is true about the overall mean of the diameter_km column after imputation?

• It is likely to be an unbiased estimate of the true mean.

• It is likely to be a biased estimate of the true mean.

Problem 3

The questions below reference the following HTML.

<html>
    <head>
        <title>ZOMBO</title>
    </head>

    <body>
        <h1>Welcome to Zombo.com</h1>
        <div id="greeting">
            <ul>
                <li>This is Zombo.com, welcome!</li>
                <li>This is Zombo.com</li>
                <li>Welcome to Zombo.com</li>
                <li>You can do anything at Zombo.com -- anything at all!</li>
                <li>The only limit is yourself.</li>
            </ul>
        </div>
        <div id="footnotes" class="faded">
            <h3>Footnotes</h3>

            <ol id="footnotes">
                <li>Please consider <a href="paypal.html">donating!</a></li>
                <li>Made in California with <a href="https://reactj.org">React.</a><li>
            </ol>
        </div>
    </body>
</html>

Problem 3.1

Consider the node representing the body tag in the Document Object Model (DOM) tree of the above HTML. How many children does this node have?

Problem 3.2

The page shown above contains five greetings, each one a list item in an unordered list. The first greeting is This is Zombo.com, welcome!, and the last is The only limit is yourself..

Suppose we have parsed the HTML into a BeautifulSoup object stored in the variable named soup.

Which of the following pieces of code will produce a list of BeautifulSoup objects, each one representing a single greeting list item? Mark all which apply.

• soup.find('div').find_all('li')

• soup.find_all('li', id='greeting')

• soup.find('div', id='greeting').find_all('li')

• soup.find_all('ul/li')

Problem 3.3

Suppose you perform an HTTP request to a web API using the requests module. The response succeeds, and you get the following (truncated) content back:

>>> resp = requests.get("https://pokeapi.co/api/v2/pokemon/squirtle")
>>> resp.content
b'{"abilities":[{"ability":{"name":"torrent","url":"https://pokeapi.co"...

What type of data has been returned?

• HTML

• JSON

• XML

• PNG

Problem 4

You are scraping a web page using requests. Your code has been working fine and returns the desired result, but suddenly you find that your code takes much longer to finish (if it finishes at all). It does not raise an exception.

What is the most likely cause of the issue?

• The page has a very large GIF that hasn’t stopped playing.

• You have made too many requests to the server in a short amount of time

• The page contains a Unicode character that requests cannot parse

• The page has suddenly changed and has caused requests to enter an infinite loop.

Problem 5

In this question, you will be asked to determine which strings are matched by various regular expression patterns when re.search is used. For these questions, remember that re.search(pattern, s) matches s if the pattern can be found anywhere in s (not necessarily at the beginning). For example, re.search("name", "my name is justin") matches, while re.search("foo", "my name is justin") does not.

Problem 5.1

Which of the below strings are matched by re.search using the pattern 'a+'? Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 5.2

Which of the below strings are matched by re.search using the pattern 'a+ b+'? Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 5.3

Which of the below strings are matched by re.search using the pattern '\baa\b'

Recall that the r at the front of the pattern string above makes it a “raw” string; this is used so that \b is not interpreted by Python as a special backspace character.

Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 5.4

Which of the below strings are matched by re.search using the pattern '(aba){2,}'? Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 5.5

Which of the below strings are matched by re.search using the pattern 'a..a'? Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 5.6

Which of the below strings are matched by re.search using the pattern '.*'? Select all that apply.

• "aa bb cc"

• "aaa bbb ccc"

• "abaaba"

• "abacaba"

Problem 6

Problem 6.1

Consider the following four sentences:

• “this is one”
• “this is two”
• “this is the third”
• “and this is the fourth”

Suppose these sentences are encoded into a “bag of words” feature representation. The result is a dataframe with four rows (one for each sentence). How many columns are in this dataframe? Your answer should be in the form of a number.

Problem 6.2

Again consider the same four sentences shown above.

What is the TF-IDF score for the word “this” in the first sentence? Use base-2 logarithm.

Your answer should be in the form of a number.

Problem 6.3

Again consider the same four sentences shown above.

What is the TF-IDF score for the word “and” in the last sentence? Use base-2 logarithm.

Your answer should be in the form of a number.

Problem 7

Problem 7.1

Consider the dataframe shown below:

Suppose you wish to use this data in a linear regression model. To do so, the color column must be encoded numerically.

True or False: a meaningful way to numerically encode the color column is to replace each string by its index in the alphabetic ordering of the colors. That is, to replace “blue” by 1, “green” by 2, and “red” by 3.

• True

• False

Problem 7.2

Suppose you perform a one-hot encoding of a Series containing the following strings:

["red", "blue", "red", "green", "green", "purple", "orange", "blue"]}

Assume that the encoding is created using the OneHotEncoder(drop='first') from sklearn. Note the drop='first' keyword argument: skearn’s documentation says that this will “drop the first category in each feature.”

How many columns will the resulting one-hot encoding table have?

Problem 8

The next four questions concern the following example.

A Silicon Valley startup candy company buys a factory from a lightbulb company and repurposes some of the existing equipment to make chocolate bars with the goal of disrupting the candy industry. Their IPO is delayed, however, when they discover that some of their chocolate bars contain broken glass.

The company’s engineers quickly build an AI which looks at the chocolate bars coming off of the conveyor belt and predicts which bars contain broken glass (“yes”) and which don’t (“no”). The results are shown in the following confusion matrix:

Problem 8.1

What is the accuracy of their model as a percentage (between 0% and 100%)?

Problem 8.2

What is the recall of their model as a percentage (between 0% and 100%)?

Problem 8.3

From a safety perspective, which metric should be maximized in this situation?

• Precision

• Recall

Problem 8.4

Suppose the company’s investors wish to improve the model’s precision. Which should they do (besides hire better data scientists)?

• Lower their model’s threshold for predicting that a bar contains glass, thus throwing out more candy.

• Raise their model’s threshold for predicting that a bar contains glass, thus throwing out less candy.

Problem 9

Problem 9.1

Suppose you split a data set into a training set and a test set. You train a classifier on the training set and test it on the test set.

True or False: the training accuracy must be higher than the test accuracy.

• True

• False

Problem 9.2

Suppose you are using sklearn to train a decision tree model to predict whether a data science student is enrolled in DSC 80 or not based on several pieces of information, including their hours spent coding per week and whether or not they have heard of the Kolmogorov-Smirnov test statistic.

Suppose you train your model, but achieve much lower training and test accuracies than you expect. When you look at the data and make predictions yourself, you are easily able to achieve higher train and test accuracies.

What should be done to improve the performance of the model?

• Decrease the max_depth hyperparameter; the model is “overfitting”.

• Increase the max_depth hyperparameter; the model is “underfitting”.

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