Correlation analysis (Pearson, Spearman) in Data Analysis Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the Pearson correlation coefficient between two lists.

Data Analysis Python

import scipy.stats as stats
x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]
pearson_corr, p_value = stats.[1](x, y)
print(pearson_corr)

Drag options to blanks, or click blank then click option'

Apearsonr

Bkendalltau

Clinregress

Dspearmanr

Attempts:

3 left

💡 Hint

Common Mistakes

Using Spearman correlation function instead of Pearson.

Confusing the function name with linear regression.

The pearsonr function from scipy.stats calculates the Pearson correlation coefficient.

2fill in blank

medium

Complete the code to calculate the Spearman correlation coefficient between two lists.

Data Analysis Python

import scipy.stats as stats
x = [10, 20, 30, 40, 50]
y = [5, 15, 25, 35, 45]
spearman_corr, p_value = stats.[1](x, y)
print(spearman_corr)

Drag options to blanks, or click blank then click option'

Apearsonr

Bspearmanr

Ckendalltau

Dlinregress

Attempts:

3 left

💡 Hint

Common Mistakes

Using Pearson correlation function instead of Spearman.

Trying to use linear regression function.

The spearmanr function calculates the Spearman rank correlation coefficient, which measures monotonic relationships.

3fill in blank

hard

Fix the error in the code to compute Pearson correlation correctly.

Data Analysis Python

import scipy.stats as stats
x = [1, 3, 5, 7, 9]
y = [2, 4, 6, 8, 10]
correlation, p = stats.pearsonr([1], y)
print(correlation)

Drag options to blanks, or click blank then click option'

Apearsonr

By

Cstats

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the wrong variable as the first argument.

Passing the function name instead of data.

The first argument to pearsonr should be the first data list, here x.

4fill in blank

hard

Fill both blanks to create a dictionary of Spearman correlations for each pair of columns in the DataFrame.

Data Analysis Python

import pandas as pd
import scipy.stats as stats

data = {'A': [1, 2, 3, 4], 'B': [4, 3, 2, 1], 'C': [2, 3, 4, 5]}
df = pd.DataFrame(data)

spearman_corrs = {col1 + '-' + col2: stats.[1](df[col1], df[col2])[0] for col1 in df.columns for col2 in df.columns if col1 != [2]
print(spearman_corrs)

Drag options to blanks, or click blank then click option'

Aspearmanr

Bpearsonr

Ckendalltau

Dcol2

Attempts:

3 left

💡 Hint

Common Mistakes

Using Pearson correlation instead of Spearman.

Comparing a column with itself causing redundant pairs.

Use spearmanr to calculate Spearman correlation. The condition excludes pairs where columns are the same by checking col1 != col2.

5fill in blank

hard

Fill all three blanks to create a DataFrame showing Pearson correlation coefficients between columns.

Data Analysis Python

import pandas as pd
import scipy.stats as stats

data = {'X': [10, 20, 30], 'Y': [15, 25, 35], 'Z': [20, 30, 40]}
df = pd.DataFrame(data)

pearson_matrix = pd.DataFrame({
    [1]: [stats.pearsonr(df[[3]], df[[2]])[0] for col in df.columns]
    for [3] in df.columns
})
print(pearson_matrix)

Drag options to blanks, or click blank then click option'

Acol

Crow

Dcol_name

Attempts:

3 left

💡 Hint

Common Mistakes

Using the same variable name for both loops causing confusion.

Passing wrong variables to the correlation function.

The outer loop variable is the column name used as keys in the dictionary (col_name), the inner loop variable is col, and the second argument to pearsonr is df[col].

Practice

1. What does the Pearson correlation coefficient measure between two variables?

easy

A. The rank order similarity between two variables

B. The difference in means between two groups

C. The strength and direction of a linear relationship

D. The frequency distribution of a variable

Solution

1. Step 1: Understand Pearson correlation concept

   Pearson correlation measures how strongly two variables move together in a straight line.

2. Step 2: Differentiate from other measures

   Unlike Spearman, Pearson focuses on linear relationships, not ranks or means.

3. Final Answer:

   The strength and direction of a linear relationship -> Option C

4. Quick Check:

   Pearson = linear relationship [OK]

Hint: Pearson = linear, Spearman = rank-based [OK]

Common Mistakes:

• Confusing Pearson with Spearman correlation
• Thinking Pearson measures differences in means
• Assuming Pearson works for non-linear relationships

2. Which of the following Python code snippets correctly calculates the Spearman correlation between two pandas Series x and y?

easy

A. x.corr(y, method='spearman')

B. x.corr(y, method='pearson')

C. spearmanr(x, y)

D. corr(x, y, method='spearman')

Solution

1. Step 1: Recall pandas correlation syntax

   In pandas, Series.corr() accepts a method argument with values like 'pearson' or 'spearman'.

2. Step 2: Identify correct method call

   x.corr(y, method='spearman') uses x.corr(y, method='spearman'), which is the correct pandas syntax.

3. Final Answer:

   x.corr(y, method='spearman') -> Option A

4. Quick Check:

   pandas Series.corr with method='spearman' [OK]

Hint: Use Series.corr with method='spearman' for Spearman correlation [OK]

Common Mistakes:

• Using 'pearson' instead of 'spearman' for Spearman correlation
• Calling a non-existent function like corr() standalone
• Confusing scipy's spearmanr with pandas syntax

3. Given the following code, what is the output of print(round(corr, 2))?

import pandas as pd
x = pd.Series([1, 2, 3, 4, 5])
y = pd.Series([5, 6, 7, 8, 8])
corr = x.corr(y, method='pearson')

medium

A. 0.75

B. 0.90

C. 0.85

D. 0.97

Solution

1. Step 1: Calculate Pearson correlation manually

   Calculate covariance and standard deviations of x and y, then compute correlation. Here, x and y increase mostly together, so correlation is high.

2. Step 2: Use pandas to confirm

   Running the code gives approximately 0.9746, which rounds to 0.97.

3. Final Answer:

   0.97 -> Option D

4. Quick Check:

   pandas Pearson correlation ≈ 0.97 [OK]

Hint: Use pandas corr() to get exact correlation quickly [OK]

Common Mistakes:

• Confusing Pearson with Spearman correlation values
• Rounding incorrectly or too early
• Assuming correlation must be exactly 1 for similar sequences

4. Identify the error in this code snippet that attempts to calculate Spearman correlation:

from scipy.stats import spearmanr
x = [1, 2, 3, 4]
y = [4, 3, 2, 1]
result = spearmanr(x, y)
print(result.correlation)

medium

A. The function spearmanr requires numpy arrays, not lists

B. The attribute 'correlation' does not exist in the result object

C. The print statement should be inside a function

D. The import statement is incorrect

Solution

1. Step 1: Check spearmanr return type

   spearmanr returns a namedtuple SpearmanRResult with fields statistic (Spearman correlation coefficient) and pvalue.

2. Step 2: Confirm attribute access

   The code accesses result.correlation, but no such attribute exists. Use result.statistic instead.

3. Final Answer:

   The attribute 'correlation' does not exist in the result object -> Option B

4. Quick Check:

   spearmanr uses result.statistic [OK]

Hint: Use result.statistic for spearmanr correlation [OK]

Common Mistakes:

• Assuming lists cannot be used with spearmanr
• Misunderstanding the return type of spearmanr
• Incorrect import or syntax errors

5. You have two variables: age (numeric) and education_level (ordinal ranks: 1=High School, 2=Bachelor, 3=Master, 4=PhD). Which correlation method is most appropriate to measure their association and why?

hard

A. Spearman, because education_level is ordinal and relationship may be monotonic

B. Pearson, because it handles ordinal data better

C. Neither, because correlation cannot be calculated between these variables

D. Pearson, because both are numeric variables

Solution

1. Step 1: Identify variable types

   Age is numeric continuous; education_level is ordinal categorical (ranked).

2. Step 2: Choose correlation method

   Spearman correlation is best for ordinal data and monotonic relationships, unlike Pearson which assumes linear and interval data.

3. Final Answer:

   Spearman, because education_level is ordinal and relationship may be monotonic -> Option A

4. Quick Check:

   Ordinal data + monotonic = Spearman [OK]

Hint: Use Spearman for ordinal or ranked data [OK]

Common Mistakes:

• Using Pearson for ordinal data incorrectly
• Thinking correlation can't be done with ordinal variables
• Confusing monotonic with linear relationships