Regression analysis in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of simple linear regression coefficients

What is the output of the following MATLAB code that fits a simple linear regression model and displays the coefficients?

MATLAB

x = (1:5)';
y = [2.2; 2.8; 3.6; 4.5; 5.1];
mdl = fitlm(x,y);
disp(mdl.Coefficients.Estimate);

A [1.5; 0.7]

B [1.39; 0.75]

C [2.0; 0.6]

D [0.5; 1.0]

💡 Hint

Look at the linear relationship between x and y and how fitlm estimates intercept and slope.

The fitlm function fits y = beta0 + beta1*x. The estimated intercept is about 1.39 and slope about 0.75 for this data.

❓ data_output

intermediate

Number of observations after removing missing data

Given the dataset with missing values, how many observations remain after removing rows with NaNs using MATLAB?

MATLAB

data = [1 2; NaN 3; 4 NaN; 5 6];
data_clean = rmmissing(data);
num_obs = size(data_clean,1);

A 2

B 4

C 3

D 1

💡 Hint

rmmissing removes any row with at least one NaN.

Rows 2 and 3 contain NaNs and are removed. Rows 1 and 4 remain, so 2 observations remain.

❓ visualization

advanced

Interpretation of residual plot

You run a linear regression and plot residuals versus fitted values. The plot shows a clear curved pattern. What does this indicate?

A Residuals are normally distributed.

B There is heteroscedasticity but no model misspecification.

C The linear model fits well with no issues.

D The model likely misses a nonlinear relationship; consider adding polynomial terms.

💡 Hint

Look for patterns in residuals to check model assumptions.

A curved pattern in residuals suggests the linear model does not capture nonlinear trends in data.

🧠 Conceptual

advanced

Effect of multicollinearity in regression

What is the main problem caused by multicollinearity among predictors in a multiple linear regression model?

A It causes the model to have perfect predictions.

B It reduces the number of predictors automatically.

C It inflates the variance of coefficient estimates, making them unstable.

D It improves the interpretability of coefficients.

💡 Hint

Think about how correlated predictors affect coefficient estimates.

Multicollinearity makes coefficient estimates sensitive to small data changes, increasing variance and reducing reliability.

🔧 Debug

expert

Identify error in MATLAB code for polynomial regression

What error does the following MATLAB code produce when fitting a polynomial regression model?

MATLAB

x = (1:5)';
y = [2; 4; 6; 8; 10];
X = [x x.^2];
mdl = fitlm(X, y);
disp(mdl.Coefficients.Estimate);

A No error; outputs coefficients including intercept and two predictors.

B Error: 'fitlm' requires a table or vector for predictors, not a matrix.

C Error: Dimension mismatch between X and y.

D Error: Missing intercept term in X matrix.

💡 Hint

Check how fitlm accepts predictor inputs.

fitlm accepts numeric matrices for predictors and automatically adds intercept. The code runs without error.

Practice

1.

What is the main purpose of regression analysis in MATLAB?

easy

A. To find relationships between variables

B. To sort data alphabetically

C. To create pie charts

D. To calculate matrix inverses

Solution

1. Step 1: Understand regression analysis goal

   Regression analysis is used to find how one variable depends on others.

2. Step 2: Match purpose with options

   Only To find relationships between variables describes finding relationships between variables, which is the goal of regression.

3. Final Answer:

   To find relationships between variables -> Option A

4. Quick Check:

   Regression = find relationships [OK]

Hint: Regression = relationship finding between numbers [OK]

Common Mistakes:

• Confusing regression with sorting or plotting
• Thinking regression calculates matrix inverses

2.

Which MATLAB command correctly fits a linear regression model to data X and response Y?

?

easy

A. mdl = fitlm(X, Y);

B. mdl = linearfit(X, Y);

C. mdl = regress(X, Y);

D. mdl = fitmodel(X, Y);

Solution

1. Step 1: Recall MATLAB function for linear regression

   The function fitlm fits linear regression models in MATLAB.

2. Step 2: Check options for correct syntax

   Only mdl = fitlm(X, Y); uses fitlm(X, Y) correctly; others are invalid or incorrect functions.

3. Final Answer:

   mdl = fitlm(X, Y); -> Option A

4. Quick Check:

   fitlm = linear model fit [OK]

Hint: Use fitlm for linear regression in MATLAB [OK]

Common Mistakes:

• Using non-existent functions like linearfit or fitmodel
• Confusing regress syntax with fitlm

3.

What is the output of this MATLAB code?

X = (1:5)';
Y = [2; 4; 6; 8; 10];
mdl = fitlm(X, Y);
disp(mdl.Coefficients.Estimate(2));

medium

A. 10

B. 2

C. 1

D. 4

Solution

1. Step 1: Understand data and model

   X is 1 to 5, Y is 2,4,6,8,10 which is Y = 2*X exactly.

2. Step 2: Interpret coefficient output

   The slope (coefficient for X) is 2, so mdl.Coefficients.Estimate(2) returns 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Slope = 2 [OK]

Hint: Slope equals change in Y over X [OK]

Common Mistakes:

• Confusing intercept with slope coefficient
• Misreading coefficient index

4.

Identify the error in this MATLAB code for regression:

X = [1 2 3 4 5];
Y = [2; 4; 6; 8; 10];
mdl = fitlm(X, Y);

medium

A. fitlm requires three input arguments

B. fitlm cannot handle numeric data

C. Y must be a matrix, not a vector

D. X and Y should be column vectors, not row vectors

Solution

1. Step 1: Check input shapes for fitlm

   fitlm expects predictors and response as column vectors or tables.

2. Step 2: Identify vector orientation

   X is a row vector and Y is a column vector; they should be column vectors for fitlm to work properly.

3. Final Answer:

   X and Y should be column vectors, not row vectors -> Option D

4. Quick Check:

   fitlm needs column vectors [OK]

Hint: Use column vectors for fitlm inputs [OK]

Common Mistakes:

• Passing row vectors instead of column vectors
• Thinking fitlm needs 3 inputs
• Believing fitlm can't handle numeric vectors

5.

You have data vectors X and Y with some outliers. Which approach in MATLAB regression helps reduce outlier impact?

hard

A. Remove all data points manually

B. Use fitlm(X, Y) without options

C. Use fitlm(X, Y, ''RobustOpts'', ''on'')

D. Use polyfit(X, Y, 2) for quadratic fit

Solution

1. Step 1: Understand outlier effect on regression

   Outliers can distort ordinary least squares regression results.

2. Step 2: Identify MATLAB option for robustness

   Using RobustOpts set to 'on' in fitlm applies robust regression reducing outlier influence.

3. Final Answer:

   Use fitlm(X, Y, ''RobustOpts'', ''on'') -> Option C

4. Quick Check:

   RobustOpts = reduce outlier impact [OK]

Hint: Add RobustOpts 'on' to fitlm for outliers [OK]

Common Mistakes:

• Ignoring outliers and using default fitlm
• Removing data points without analysis
• Using polynomial fit which may not reduce outliers