Correlation with corr() in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this correlation calculation?

Given the following DataFrame, what is the output of df.corr()?

Data Analysis Python

import pandas as pd
import numpy as np

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

A {'A': {'A': 1.0, 'B': -1.0, 'C': 0.0}, 'B': {'A': -1.0, 'B': 1.0, 'C': 0.0}, 'C': {'A': 0.0, 'B': 0.0, 'C': 1.0}}

B

     A    B    C
A  1.0 -1.0  0.0
B -1.0  1.0  0.0
C  0.0  0.0  1.0

C

     A    B    C
A  1.0  1.0  0.0
B  1.0  1.0  0.0
C  0.0  0.0  1.0

D

     A    B    C
A  1.0 -1.0  1.0
B -1.0  1.0 -1.0
C  1.0 -1.0  1.0

💡 Hint

Remember that correlation measures how two variables move together. Negative means opposite directions.

Column A and B are perfectly negatively correlated (-1.0). Column C does not correlate with A or B (0.0). The diagonal is always 1.0 because a variable correlates perfectly with itself.

❓ data_output

intermediate

How many pairs have correlation above 0.5?

Using the DataFrame below, how many unique pairs of columns have a correlation greater than 0.5?

Data Analysis Python

import pandas as pd
import numpy as np
np.random.seed(0)
data = {'X': np.random.rand(10), 'Y': np.random.rand(10), 'Z': np.random.rand(10)}
df = pd.DataFrame(data)
corr_matrix = df.corr()
# Count pairs with correlation > 0.5 (excluding self-correlation)
count = 0
for i in corr_matrix.columns:
    for j in corr_matrix.columns:
        if i < j and corr_matrix.loc[i,j] > 0.5:
            count += 1
print(count)

A 0

B 1

C 2

D 3

💡 Hint

Random numbers usually have low correlation unless seeded or constructed.

The random columns X, Y, Z are independent. Their correlations are close to zero, so no pairs exceed 0.5.

🔧 Debug

advanced

What error does this code raise?

What error will this code raise when trying to compute correlation?

Data Analysis Python

import pandas as pd
data = {'A': [1, 2, 3], 'B': ['x', 'y', 'z']}
df = pd.DataFrame(data)
print(df.corr())

A TypeError: unsupported operand type(s) for -: 'str' and 'int'

B ValueError: could not convert string to float: 'x'

C Empty DataFrame with columns and index but no data

D No error, 1x1 correlation matrix with value 1.0

💡 Hint

Correlation only works on numeric columns; non-numeric columns are ignored.

Pandas automatically excludes non-numeric columns when computing correlation. So no error occurs, but columns with strings are ignored. The result is a correlation matrix for numeric columns only.

🚀 Application

advanced

Which column pair has the strongest positive correlation?

Given the DataFrame below, which pair of columns has the strongest positive correlation?

Data Analysis Python

import pandas as pd
data = {'P': [1, 2, 3, 4, 5], 'Q': [2, 4, 6, 8, 10], 'R': [5, 4, 3, 2, 1], 'S': [1, 3, 1, 7, 9]}
df = pd.DataFrame(data)
corr = df.corr()
print(corr)

A Q and R

B P and R

C P and Q

D P and S

💡 Hint

Look for pairs where one column is a perfect multiple of the other.

Column Q is exactly 2 times column P, so their correlation is 1.0 (perfect positive). Other pairs have lower or negative correlation.

🧠 Conceptual

expert

What does a correlation value of 0 indicate?

In the context of the corr() method, what does a correlation value of 0 between two variables mean?

A The two variables have no linear relationship

B The two variables are independent in all ways

C The two variables have a perfect positive linear relationship

D The two variables have a perfect negative linear relationship

💡 Hint

Correlation measures linear relationships only.

A correlation of 0 means no linear relationship exists between the variables. However, they might still have a non-linear relationship or be dependent in other ways.

Practice

1. What does the corr() function in pandas do?

easy

A. Counts the number of missing values in a DataFrame

B. Calculates the correlation between numeric columns in a DataFrame

C. Sorts the DataFrame by a specific column

D. Filters rows based on a condition

Solution

1. Step 1: Understand the purpose of corr()

   The corr() function calculates how numeric columns relate to each other in a DataFrame.

2. Step 2: Compare with other options

   Counting missing values, sorting, or filtering are different functions like isna(), sort_values(), and loc.

3. Final Answer:

   Calculates the correlation between numeric columns in a DataFrame -> Option B

4. Quick Check:

   corr() finds relationships [OK]

Hint: Remember: corr() measures how numbers move together [OK]

Common Mistakes:

• Confusing corr() with counting or sorting functions
• Thinking corr() works on non-numeric data
• Assuming corr() changes the DataFrame structure

2. Which of the following is the correct way to calculate correlation between columns in a pandas DataFrame named df?

easy

A. df.corr()

B. df.correlate()

C. df.corrrelation()

D. df.correlation()

Solution

1. Step 1: Recall the exact method name

   The correct pandas method to calculate correlation is corr().

2. Step 2: Check each option

   Options A, B, and C are misspelled or incorrect method names.

3. Final Answer:

   df.corr() -> Option A

4. Quick Check:

   Use df.corr() for correlation [OK]

Hint: Remember exact method name: corr() not correlation [OK]

Common Mistakes:

• Misspelling the method name
• Using non-existent pandas methods
• Confusing corr() with other functions

3. Given the following DataFrame df:

   A  B  C
0  1  2  5
1  2  4  7
2  3  6  9
3  4  8  11

What is the output of df.corr()?

medium

A. {'A': {'A': 1.0, 'B': 1.0, 'C': 1.0}, 'B': {'A': 1.0, 'B': 1.0, 'C': 1.0}, 'C': {'A': 1.0, 'B': 1.0, 'C': 1.0}}

B. {'A': {'A': 1.0, 'B': 0.5, 'C': 0.5}, 'B': {'A': 0.5, 'B': 1.0, 'C': 0.5}, 'C': {'A': 0.5, 'B': 0.5, 'C': 1.0}}

C. {'A': {'A': 1.0, 'B': -1.0, 'C': 0.0}, 'B': {'A': -1.0, 'B': 1.0, 'C': 0.0}, 'C': {'A': 0.0, 'B': 0.0, 'C': 1.0}}

D. Error: corr() cannot be applied to this DataFrame

Solution

1. Step 1: Understand the data pattern

   Columns A, B, and C increase perfectly linearly: B = 2*A, C = 2*A + 3.

2. Step 2: Calculate correlation values

   Since all columns are perfectly linearly related, correlation between any two is 1.0, and correlation with itself is 1.0.

3. Final Answer:

   {'A': {'A': 1.0, 'B': 1.0, 'C': 1.0}, 'B': {'A': 1.0, 'B': 1.0, 'C': 1.0}, 'C': {'A': 1.0, 'B': 1.0, 'C': 1.0}} -> Option A

4. Quick Check:

   Perfect linear relation means correlation = 1 [OK]

Hint: Perfect linear columns have correlation 1 [OK]

Common Mistakes:

• Assuming correlation less than 1 for perfect linear data
• Confusing correlation with covariance
• Thinking corr() raises error on numeric data

4. You run the code below but get an error:

import pandas as pd
df = pd.DataFrame({'X': [1, 2, 3], 'Y': ['a', 'b', 'c']})
print(df.corr(numeric_only=False))

What is the cause of the error?

medium

A. The corr() method is misspelled

B. The DataFrame is empty

C. The DataFrame has non-numeric columns which corr() cannot process

D. The DataFrame columns have missing values

Solution

1. Step 1: Analyze DataFrame columns

   Column 'Y' contains strings, which are non-numeric.

2. Step 2: Understand corr() requirements

   corr() only works on numeric columns; non-numeric columns cause it to ignore or error depending on pandas version.

3. Final Answer:

   The DataFrame has non-numeric columns which corr() cannot process -> Option C

4. Quick Check:

   corr() needs numeric data [OK]

Hint: Check for non-numeric columns before using corr() [OK]

Common Mistakes:

• Assuming corr() works on strings
• Thinking misspelling caused error
• Ignoring data types in DataFrame

5. You have a DataFrame df with columns height, weight, and age. You want to find which two variables have the strongest positive correlation. Which code snippet correctly finds this?

hard

A. corr_matrix = df.corr()
max_corr = corr_matrix.where(corr_matrix < 1).max().max()

B. corr_matrix = df.corr()
max_corr = corr_matrix.where(corr_matrix != 1).min().min()

C. corr_matrix = df.corr()
max_corr = corr_matrix.max().max()

D. corr_matrix = df.corr()
max_corr = corr_matrix.where(corr_matrix != 1).max().max()

Solution

1. Step 1: Calculate correlation matrix

   Use df.corr() to get correlations between all numeric columns.

2. Step 2: Exclude self-correlation (which is 1)

   Use where(corr_matrix != 1) to ignore diagonal 1s, then find the maximum correlation value.

3. Step 3: Find the strongest positive correlation

   Use max().max() to get the highest correlation excluding 1.

4. Final Answer:

   corr_matrix = df.corr() max_corr = corr_matrix.where(corr_matrix != 1).max().max() -> Option D

5. Quick Check:

   Exclude 1, then find max correlation [OK]

Hint: Exclude 1s (self-correlation) before max() [OK]

Common Mistakes:

• Including diagonal 1s in max correlation
• Using min() instead of max()
• Not excluding self-correlation values