Correlation and covariance in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the covariance matrix of matrix A.

MATLAB

covMatrix = [1](A);

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

Avar

Bcorr

Cmean

Dcov

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'corr' instead of 'cov' will compute correlation, not covariance.

Using 'mean' or 'var' will not produce a covariance matrix.

The cov function computes the covariance matrix of the input matrix.

2fill in blank

medium

Complete the code to calculate the correlation coefficient between vectors x and y.

MATLAB

r = [1](x, y);

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

Acorrcoef

Bcov

Ccorr

Dmean

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'cov' returns covariance, not correlation.

Using 'mean' is unrelated to correlation.

The corrcoef function returns the correlation coefficient matrix between vectors.

3fill in blank

hard

Fix the error in the code to compute covariance between vectors a and b.

MATLAB

covAB = cov([1]);

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

A[a; b]

Ba, b

C[a, b]

Da + b

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'a, b' is invalid syntax.

Using '[a; b]' concatenates vertically, which is incorrect here.

The cov function requires a matrix input where each column is a variable. Using [a, b] concatenates vectors as columns.

4fill in blank

hard

Fill both blanks to create a dictionary (struct) that maps variable names to their covariance values.

MATLAB

covStruct = struct('[1]', covMatrix(1,2), '[2]', covMatrix(2,1));

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

Avar1

Bvar2

Ccov12

Dcov21

Attempts:

3 left

💡 Hint

Common Mistakes

Using variable names instead of covariance names for struct fields.

Mixing up field names with variable names.

Struct fields should be named to represent covariance values between variables, such as 'cov12' and 'cov21'.

5fill in blank

hard

Fill all three blanks to compute the correlation matrix and extract the correlation coefficient between variables 1 and 2.

MATLAB

corrMatrix = [1](data);
r12 = corrMatrix([2], [3]);

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

Acov

B1

C2

Dcorrcoef

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'cov' instead of 'corrcoef' for correlation matrix.

Mixing up row and column indices.

Use corrcoef to compute the correlation matrix. Then extract the element at row 1, column 2 for the correlation coefficient.

Practice

1.

What does the MATLAB function cov compute?

easy

A. Standard deviation of a variable

B. Covariance matrix showing how two variables vary together

C. Mean value of a dataset

D. Correlation coefficient between two variables

Solution

1. Step 1: Understand the purpose of cov

   The cov function calculates the covariance matrix, which shows how two variables change together.

2. Step 2: Differentiate covariance from correlation

   Correlation measures strength and direction, but cov specifically returns covariance values.

3. Final Answer:

   Covariance matrix showing how two variables vary together -> Option B

4. Quick Check:

   cov = covariance matrix [OK]

Hint: Remember: cov = covariance matrix, corrcoef = correlation [OK]

Common Mistakes:

• Confusing covariance with correlation
• Thinking cov returns a single value instead of a matrix
• Mixing up cov with mean or std functions

2.

Which of the following is the correct syntax to calculate the correlation matrix of variables X and Y in MATLAB?

?

easy

A. R = cov(X, Y);

B. R = correlation(X, Y);

C. R = corrcoef(X, Y);

D. R = corr(X, Y);

Solution

1. Step 1: Identify MATLAB function for correlation

   The correct MATLAB function to compute correlation coefficients is corrcoef.

2. Step 2: Check syntax correctness

   The syntax R = corrcoef(X, Y); correctly computes the correlation matrix between X and Y.

3. Final Answer:

   R = corrcoef(X, Y); -> Option C

4. Quick Check:

   corrcoef syntax = R = corrcoef(X, Y) [OK]

Hint: Use corrcoef for correlation, not cov [OK]

Common Mistakes:

• Using cov instead of corrcoef for correlation
• Using non-existent functions like correlation or corr
• Missing parentheses or semicolon

3.

What is the output of the following MATLAB code?

X = [1 2 3];
Y = [4 5 6];
R = corrcoef(X, Y);
disp(R);

medium

A. [[1 0]; [0 1]]

B. [[1 0.5]; [0.5 1]]

C. [[1 -1]; [-1 1]]

D. [[1 1]; [1 1]]

Solution

1. Step 1: Understand the data vectors

   Vectors X and Y are perfectly linearly related: Y = X + 3.

2. Step 2: Calculate correlation coefficient

   Since they have a perfect positive linear relationship, correlation coefficient is 1.

3. Final Answer:

   [[1 1]; [1 1]] -> Option D

4. Quick Check:

   Perfect positive correlation = 1 [OK]

Hint: Perfect linear relation means correlation = 1 [OK]

Common Mistakes:

• Assuming correlation less than 1 for linear relation
• Confusing covariance with correlation values
• Misreading matrix output format

4.

Identify the error in this MATLAB code snippet:

X = [1 2 3];
Y = [4 5 6];
R = corrcoef(X Y);
disp(R);

medium

A. Missing comma between X and Y in corrcoef function

B. Vectors X and Y must be column vectors

C. corrcoef cannot take two inputs

D. disp cannot display matrices

Solution

1. Step 1: Check function call syntax

   The function call corrcoef(X Y) is missing a comma between X and Y.

2. Step 2: Confirm correct syntax

   The correct syntax is corrcoef(X, Y) with a comma separating inputs.

3. Final Answer:

   Missing comma between X and Y in corrcoef function -> Option A

4. Quick Check:

   Function arguments need commas [OK]

Hint: Separate function arguments with commas [OK]

Common Mistakes:

• Omitting commas between function arguments
• Thinking vectors must be columns for corrcoef
• Believing disp cannot show matrices

5.

You have two datasets A = [1 2 3 4] and B = [2 4 6 8]. You want to check if B is exactly twice A using correlation and covariance. Which MATLAB code snippet correctly confirms this?

hard

A. covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB(2,1)); disp(corrAB(2,1));

B. covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB); disp(corrAB);

C. covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB(1,2)); disp(corrAB(1,2));

D. covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB(1,1)); disp(corrAB(1,1));

Solution

1. Step 1: Calculate covariance and correlation matrices

   Using cov(A, B) and corrcoef(A, B) returns 2x2 matrices with variances/covariances and correlations.

2. Step 2: Extract covariance and correlation between A and B

   The off-diagonal elements (1,2) or (2,1) give covariance and correlation between A and B.

3. Step 3: Confirm correct display of these values

   covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB(2,1)); disp(corrAB(2,1)); correctly displays covAB(2,1) and corrAB(2,1), confirming the relationship.

4. Final Answer:

   covAB = cov(A, B); corrAB = corrcoef(A, B); disp(covAB(2,1)); disp(corrAB(2,1)); -> Option A

5. Quick Check:

   Use off-diagonal elements for covariance and correlation [OK]

Hint: Off-diagonal matrix elements show variable relationships [OK]

Common Mistakes:

• Displaying entire matrix instead of specific covariance/correlation
• Using diagonal elements which are variances
• Confusing matrix indices