Arctic Sea Ice Extent: Data Analysis and Visualization ISTA 131 Hw7, Due...

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Arctic Sea Ice Extent: Data Analysis and Visualization

ISTA 131 Hw7, Due 3/30/2023 at 11:59 pm

Introduction.

This homework is the last in a three-assignment arc intended to introduce you to dealing

with data that is stored on disk in csv format using pandas. In this assignment, you will analyze the

Arctic sea ice extent data and use your analysis to predict the date the ice will disappear altogether. You

will do this by fitting lines to the March and September data. This is called simple linear regression,

calculated using ordinary least squares. You will also recalculate the data as the anomaly. The anomaly

is the difference between a given data point and the mean. In this case, we are interested in the

maximum ice extent, which occurs in March but varies from year to year as to the exact day, and the

minimum ice extent, which happens in September. Therefore, we are going to look at those months as

single entities, i.e. the March and September means for each year. In other words, instead of looking at

daily data, we will be looking at monthly data (the mean of the daily data for the month). To get the

anomaly for the monthly data, we will calculate the difference between the monthly mean for a given

year and the mean of the means for all of the years. For example, you will be calculating the difference

between the mean of the March data for 1981 and the mean of the March means for all of the years.

Looking at the anomaly instead of the absolute values will allow you to create a better visualization that

compares how ice behavior is changing in March with how ice behavior is changing in September.

Instructions.

Create a module named

hw7.py

. Below is the spec for six functions. Implement them

and upload your module to D2L Assignments.

Testing.

Download

hw7_test.py

and auxiliary testing files and put them in the same folder as your

hw7.py

module. Each of the first three functions is worth 20% of your total score. You do not directly

receive points for

main

, but it has to work correctly or you will get no points for two of your other

functions. You can examine the test module in a text editor to understand better what your code should

do. The test module is part of the spec. The test file we will use to grade your program will be different

and may uncover failings in your work not evident upon testing with the provided file. Add any

necessary tests to make sure your code works in all cases.

Documentation.

Your module must contain a header docstring containing your name, your section

leader’s name, the date,

ISTA 131 Hw7

, and a brief summary of the module. Each function must

contain a docstring. Each docstring should include a description of the function’s purpose, the name,

type, and purpose of each parameter, and the type and meaning of the function’s return value.

Grading.

Your module will be graded on correctness, documentation, and coding style. Code should be

clear and concise. You will only lose style points if your code is a real mess. Include inline comments to

explain tricky lines and summarize sections of code.

Collaboration.

Collaboration is allowed. You are responsible for your learning. Depending too much on

others will hurt you on the tests. “Helping” others too much harms them in reality. Cite any

sources/collaborators in your header docstring. Leaving this out is dishonest.

Resources.

http://statsmodels.sourceforge.net/devel/examples/notebooks/generated/ols.html

http://statsmodels.sourceforge.net/devel/generated/statsmodels.regression.linear_model.RegressionR

esults.html?highlight=regressionresults

http://statsmodels.sourceforge.net/devel/example_formulas.html

https://docs.python.org/3/library/math.html

get_Mar_Sept_frame

: This functions takes no arguments. Read

data_79_21.csv

into a hw4

frame. Recall that it looks like this:

Use it to create and return a frame that looks like this:

If you find yourself creating an empty

DataFrame

and filling in positions one at a time (it can be

avoided), make sure that your new elements are of type

np.float64

by passing the optional

argument by keyword

dtype=np.float64

when you call the

DataFrame

constructor. You will

need to include the statement

import numpy as np

at the top of your module.

get_ols_parameters

: This function takes a

Series

, fits a line to it, and returns the slope,

intercept,

R

2

, and the p-value in a list. If you stored your return value from

model.fit()

like this:

results = model.fit()

Then the p-value you want to return is in

results.pvalues['x1']

. The rest of the parameters can

be found in the Hw7 notebook.

make_prediction

: The signature for this function should look exactly like this:

def make_prediction(params, description='x-intercept:', x_name='x',

y_name='y', ceiling=False):

The

default arguments

provided with for each of the last four parameters makes passing corresponding

arguments optional. You can see calls to this function without corresponding arguments in the test, if

you wish.

Calculate the

x

-intercept (the value of

x

for which

y

= 0) using the OLS parameters contained in the first

argument. If the last argument is

True

, round the intercept up to the nearest integer >=

x

-intercept

(hint:

math.ceil

). Print your result in the format shown by this example call and its resulting output:

The first line is the description parameter followed by the

x

-intercept. The number at the beginning of

the second line (

79

in this example) is calculated using

R

2

. Round it using Python's built-in

round

function with one argument. You will also have to the use the

y_name

and

x_name

parameters to

construct the second sentence.

round(x)

returns an integer unless

x

is type

np.float64

, in which

case you get an

np.float64

. Hence the

'.0'

in this example, but not in the test examples. Round

the significance level to 1 decimal place. The message should say "

This result is not

statistically significant."

if the p-value is > 0.05.

make_fig_1

: This function takes a March-September frame (the return value from the first function),

and creates a figure that looks like the image below. The rubric for this figure:

•

+1 each:

x

and

y

tick labels are correct.

•

+3 each: the two curves look like the image.

•

+4: the

y

-axis title looks like the image. Superscripts required for any title points.

•

+4 each: the two lines look like the image.

make_fig_2

: This function takes a March-September frame, and creates a figure that looks like the

image below. The rubric for this figure:

•

+1 each:

x

and

y

tick labels are correct.

•

+3 each: the two curves look like the image.

•

+2: the

y

-axis title looks like the image. Superscripts required for any title points.

•

+2: the title looks like the image.

•

+4 each: the two lines look like the image.

main

: Get the March-September frame. Get your OLS parameters for the two means curves. Make

your predictions for winter and summer, printing a blank line between them. Make your figures and call

plt.show()

to draw them. If the predictions don't print before the plots show up when

main

is run,

Arctic Sea Ice Extent: Data Analysis and VisualizationISTA 131 Hw7, Due 3/30/2023 at 11:59 pmIntroduction.This homework is the last in a three-assignment arc intended to...

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