I make these notes available with the intent of making it easier to plan and/or take notes from class.
Student facing resources for each topic are all available at vknight.org/cfm/.
After this meeting students should:
statsmodels library to fit a line to data.Explain to students that we will be solving the following problem:
I want to know if there is a relationship between distance from home and
expectation of grade in first year mathematics students.
The variables:
- $x$ is the self reported expectation (between 0 and 100)
- $y$ is the distance from home (as a percentage of 13,000 miles which is how far New
Zealand is).
1. Obtain the following summary statistics for both $x$ and $y$:
- The mean;
- The median;
- The quartiles;
- The standard deviation;
2. Obtain the Pearson correlation coefficient between $x$ and $y$.
3. Obtain a line of best fit $y=ax + b$.
If possible, use a web form to get students to input their own data. A quick script like the following can be used to transform the data in to tuples:
import pandas as pd
df = pd.read_excel(
"/Users/smavak/Downloads/Relationship between distance from home and
grade?(1-3).xlsx"
)
x = tuple(df["What year 1 average do you think you will get this year?"])
y = tuple(df["How far is home? (Miles)"])
Here is some data that would work if not:
>>> x = (44,
... 47,
... 64,
... 67,
... 67,
... 9,
... 83,
... 21,
... 36,
... 87,
... 70,
... 88,
... 88,
... 12,
... 58,
... 65,
... 39,
... 87,
... 46,
... 88,
... 81,
... 37,
... 25,
... 77,
... 72,
... 9,
... 20,
... 80,
... 69,
... 79,
... 47,
... 64,
... 82,
... 99,
... 88,
... 49,
... 29,
... 19,
... 19,
... 14,
... 39,
... 32,
... 65,
... 9,
... 57,
... 32,
... 31,
... 74,
... 23,
... 35,
... 75,
... 55,
... 28,
... 34,
... 0,
... 0,
... 36,
... 53,
... 5,
... 38,
... )
>>> y = (17,
... 79,
... 4,
... 42,
... 58,
... 31,
... 1,
... 65,
... 41,
... 57,
... 35,
... 11,
... 46,
... 82,
... 91,
... 0,
... 14,
... 99,
... 53,
... 12,
... 42,
... 84,
... 75,
... 68,
... 6,
... 68,
... 47,
... 3,
... 76,
... 52,
... 78,
... 15,
... 20,
... 99,
... 58,
... 23,
... 79,
... 13,
... 85,
... 48,
... 49,
... 69,
... 41,
... 35,
... 64,
... 95,
... 69,
... 94,
... 0,
... 50,
... 36,
... 34,
... 48,
... 93,
... 3,
... 98,
... 42,
... 77,
... 21,
... 73,
... )
Here is what this looks like (highlight that plotting is not part of this chapter – point students at pfm chapter on matplotlib):
import matplotlib.pyplot as plt
plt.figure()
plt.scatter(x, y)
plt.xlabel("Expected grade")
plt.ylabel("Distance from home")
Compute the summary statistics:
>>> import statistics as st
>>> st.mean(x)
49.1
>>> st.median(x)
47.0
>>> st.quantiles(x, n=4)
[28.25, 47.0, 73.5]
>>> st.stdev(x) # doctest: +ELLIPSIS
27.2096...
>>> st.mean(y) # doctest: +ELLIPSIS
49.4666...
>>> st.median(y)
48.5
>>> st.quantiles(y, n=4)
[21.5, 48.5, 75.75]
>>> st.stdev(y) # doctest: +ELLIPSIS
29.9510...
Compute the Pearson coefficient of correlation:
>>> st.correlation(x, y) # doctest: +ELLIPSIS
-0.10957...
This low but negative coefficient indicates that students who are further away expect to do worst. (Note the data here is just random noise.)
Let us fit a line:
>>> slope, intercept = st.linear_regression(x, y)
>>> slope # doctest: +ELLIPSIS
-0.1206...
>>> intercept # doctest: +ELLIPSIS
55.3890...
Highlight here that we are not doing any analysis of whether or not this is a GOOD fit.
Here is what this looks like (highlight that plotting is not part of this chapter – point students at pfm chapter on matplotlib):
plt.figure()
plt.scatter(x, y)
plt.plot((0, 100), (intercept, 100 * slope + intercept), color="black")
plt.xlabel("Expected grade")
plt.ylabel("Distance from home")
Come back: with time take any questions.
Point at resources.
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