Lab 12 Solutions

Solutions: You can find the file with solutions for all questions here.

Review on HOFs

Question 1: Polynomial

A polynomial function is a function with coefficients, variables and constants. A polynomial function is said to be the nth degree polynomial if there is a term in the function with the variable to the nth degree. For example, a 4th degree polynomial must contain the term x^4 with some coefficient multiplied to it.

Complete the function polynomial, which takes in a degree and a list of coefficients. The function should output the corresponding polynomial function. 

def polynomial(degree, coeffs):
    """
    >>> fourth = polynomial(4, [3,6,2,1, 100])
    >>> fourth(3)   # 3*(3**4) + 6*(3**3) + 2*(3**2) + 1*(3**1) + 100
    526
    >>> third = polynomial(3, [2, 0, 0, 0])
    >>> third(4)   # 2*(4**3) + 0*(4**2) + 0*(4**1) + 0
    128
    """

    "*** YOUR CODE HERE ***"
    return ______

    # Option 1
    return lambda x: sum([coeffs[i]*(x ** (degree - i)) for i in range(degree + 1)])
    # Option 2
    def poly_func(x):
        return sum([coeffs[i]*(x ** (degree - i)) for i in range(degree + 1)])
    return poly_func

Use OK to test your code:

python3 ok -q polynomial --local

Question 2: Regression

Remember regression from Data 8? Here, we will build a regression model function together step-by-step in Python.

For Data8's lecture on linear regression, look here

To calculate standard units, search here

A note on testing and assert statements.

Assert statements are a good way to make sure that your function is working the way you want it to work. You can use assert statement two ways, with or without an error message. To use it without an error message:

>>> assert len([1,2,3]) == 3

If the assertion statement pass (i.e., there is no problem with your statement), nothing happens. But if your statement does not hold true, AssertionError will be displayed.

To use assert statement with an error message, add a string after a comma:

>>> assert len([1,2,3]) == 3, "Length of list is not 3!!!!!!!"

Instead of AssertionError, your string message will be displayed instead.

Complete these functions below. No doctests will be provided except for the regression function, so fill your test functions with assert statements to make sure your code works. Some examples have been provided. testregression is optional, but it's a good practice!

def mean(x):
	"""
	Return the mean of x, where x is a list of data points.

	"""

	"*** YOUR CODE HERE ***"
	return ""

	return sum(x)/len(x)

def testmean():
	assert mean([0,0,0,0,0]) == 0, "please pass me!"

	"""***PUT YOUR TEST HERE***"""

def sd(x):
	"""
	Return the standard deviation of x, where x is a list of data points.

	"""

	"*** YOUR CODE HERE ***"
	return ""

	avg = mean(x)
	result = sum([(each-avg)**2 for each in x])
	return (result/len(x))**(1/2)


def testsd():
	assert sd([0,0,0,0,0]) == 0, "pass me please!"

	"""***PUT YOUR TEST HERE***"""

def standard_units(x):
	"""
	Return the standard units of x, where x is a list of data points.
	"""

	"*** YOUR CODE HERE ***"
	return ""

	avg = mean(x)
	stand_dev = sd(x)
	result = [(each-avg)/stand_dev for each in x]
	return result

def testsu():
	"""***PUT YOUR TEST HERE***"""

def corr_coeff(x, y):
	"""
	Return the correlation coefficients (r) of x and y, where x is a list of
	data points and y is a list of data points corresponding to x.

	"""

	"*** YOUR CODE HERE ***"
	return ""

	x_stand = standard_units(x)
	y_stand = standard_units(y)
	product = [x_stand[i]*y_stand[i] for i in range(len(x_stand))]
	return mean(product)

def testcorr_coeff():
	"""***PUT YOUR TEST HERE***"""

def regression(points):
    """
    Return a function that takes in x and predicts y, based on a linear regression model.

    >>> tempVIcecream = [[35,1], [33,2], [37,3], [45,5],[47,6],[42,8],[43,9],[51,10]]
    >>> predictor = regression(tempVIcecream)
    >>> predictor(62)    # Round to the third decimal place
    14.597
    """

    "*** YOUR CODE HERE ***"
    return ""

    x = [point[0] for point in points]
    y = [point[1] for point in points]
    def model(given):
    	r = corr_coeff(x, y)
    	sd_x = sd(x)
    	sd_y = sd(y)
    	mean_x = mean(x)
    	mean_y = mean(y)
    	slope = r*(sd_y/sd_x)
    	intercept = mean_y - slope*mean_x
    	return round(slope*given+intercept, 3)
    return model


def testregression():
	"""***PUT YOUR TEST HERE***"""

Use OK to test your code:

python3 ok -q regression --local

SQLite

Setup

The simplest way to start using SQLite is to download a precompiled binary from the SQLite website. The latest version of SQLite at the time of writing is 3.24.0, but you can check for additional updates on the website.

Windows

  1. Visit the download page linked above and navigate to the section Precompiled Binaries for Windows. Click on the link sqlite-tools-win32-x86-*.zip to download the binary.
  2. Unzip the file. There should be a sqlite3.exe file in the directory after extraction.

  3. Navigate to the folder containing the sqlite3.exe file and check that the version is at least 3.8.3:

    $ cd path/to/sqlite
$ ./sqlite3 --version
3.12.1 2016-04-08 15:09:49 fe7d3b75fe1bde41511b323925af8ae1b910bc4d

MacOS Yosemite (10.10) or newer

SQLite comes pre-installed. Check that you have a version that's greater than 3.8.3:

$ sqlite3
SQLite version 3.8.10.2

Mac OS X Mavericks (10.9) or older

SQLite comes pre-installed, but it is the wrong version.

  1. Visit the download page linked above and navigate to the section Precompiled Binaries for Mac OS X (x86). Click on the link sqlite-tools-osx-x86-*.zip to download the binary.
  2. Unzip the file. There should be a sqlite3 file in the directory after extraction.

  3. Navigate to the folder containing the sqlite3 file and check that the version is at least 3.8.3:

    $ cd path/to/sqlite
$ ./sqlite3 --version
.12.1 2016-04-08 15:09:49 fe7d3b75fe1bde41511b323925af8ae1b910bc4d

Ubuntu

The easiest way to use SQLite on Ubuntu is to install it straight from the native repositories (the version will be slightly behind the most recent release):

$ sudo apt install sqlite3
$ sqlite3 --version
3.8.6 2014-08-15 11:46:33 9491ba7d738528f168657adb43a198238abde19e

Usage

You can start an interactive SQLite session in your Terminal or Git Bash with the following commands:

  • Ubuntu / Mac OS X (Yosemite or newer)

    sqlite3

  • Windows / Mac OS X (Mavericks or older)

    ./sqlite3

While the interpreter is running, you can type .help to see some of the commands you can run.

To exit out of the SQLite intepreter, type .exit or .quit or press Ctrl-C. Remember that if you see ...> after pressing return, you probably forgot a ;.

You can also run all the statements in a .sql file by doing the following:

  1. Runs your code and then exits SQLite immediately afterwards.

    1. Ubuntu / Mac OS X (Yosemite or newer)

      sqlite3 < lab12.sql

    2. Windows / Mac OS X (Mavericks or older)

      ./sqlite3 < lab12.sql

  2. Runs your code and then opens an interactive SQLite session, which is similar to running Python code with the interactive -i flag.

    1. Ubuntu / Mac OS X (Yosemite or newer)

      sqlite3 --init lab12.sql

    2. Windows / Mac OS X (Mavericks or older)

      ./sqlite3 --init lab12.sql