Regression analysis in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to fit a linear regression model using the fitlm function.

MATLAB

mdl = fitlm(X, [1]);

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

Ay

BX

Cmodel

Ddata

Attempts:

3 left

💡 Hint

Common Mistakes

Using X as the response variable instead of y.

Using a variable not defined in the workspace.

The fitlm function fits a linear model to predictors X and response y. So y is the response variable.

2fill in blank

medium

Complete the code to predict new values using the trained model.

MATLAB

y_pred = predict([1], X_new);

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

Ay

BX

Cmdl

Dfitlm

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the predictor matrix X instead of the model object.

Passing the response variable y instead of the model.

The predict function uses the trained model object mdl to predict new responses.

3fill in blank

hard

Fix the error in the code to extract the R-squared value from the model.

MATLAB

R2 = mdl.[1];

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

ARsquared.Ordinary

BModelFit

CFit

DCoefficients

Attempts:

3 left

💡 Hint

Common Mistakes

Using Coefficients property which holds regression coefficients.

Using ModelFit or Fit which are not valid properties.

The R-squared value is stored in the Rsquared.Ordinary property of the fitted model object.

4fill in blank

hard

Fill both blanks to create a scatter plot of data and overlay the regression line.

MATLAB

scatter(X, y);
hold on;
plot(X, mdl.[1](2) * X + mdl.[2](1));
hold off;

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

ACoefficients.Estimate

BCoefficients

CEstimate

DStats

Attempts:

3 left

💡 Hint

Common Mistakes

Using Coefficients directly without .Estimate.

Using Stats which is not a valid property for coefficients.

The regression line is plotted using the slope and intercept from Coefficients.Estimate. The intercept is the first element Coefficients.Estimate(1), slope the second Coefficients.Estimate(2).

5fill in blank

hard

Fill all three blanks to compute residuals and plot them.

MATLAB

residuals = y - predict([1], [2]);
figure;
plot([3], residuals, 'o');
xlabel('Predictor');
ylabel('Residuals');

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

Amdl

BX

Cy

DX_new

Attempts:

3 left

💡 Hint

Common Mistakes

Using y instead of X for prediction input.

Plotting residuals against y instead of predictors.

Residuals are actual y minus predicted values from model mdl using predictors X. The residuals are plotted against X.

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