Regression analysis in MATLAB

Introduction

Regression analysis helps us find the relationship between numbers. It shows how one number changes when another changes.

Predicting house prices based on size and location.

Estimating sales based on advertising budget.

Understanding how temperature affects ice cream sales.

Finding the link between study hours and exam scores.

Syntax

MATLAB

mdl = fitlm(X, y);

% X is the input data (predictors)
% y is the output data (response)
% mdl is the regression model object

Use fitlm to create a linear regression model.

X can be a vector or matrix of predictors, y is the response vector.

Examples

Simple linear regression with one predictor.

MATLAB

x = [1; 2; 3; 4; 5];
y = [2; 4; 5; 4; 5];
mdl = fitlm(x, y);

Multiple linear regression with two predictors.

MATLAB

X = [1 2; 2 3; 3 4; 4 5; 5 6];
y = [3; 5; 7; 9; 11];
mdl = fitlm(X, y);

Sample Program

This program fits a linear regression model to the data and shows the results.

MATLAB

x = [1; 2; 3; 4; 5];
y = [2; 4; 5; 4; 5];
mdl = fitlm(x, y);
disp(mdl);

Important Notes

Check the R-squared value to see how well the model fits the data.

Look at p-values to understand if predictors are meaningful.

More data points usually give better models.

Summary

Regression analysis finds relationships between numbers.

Use fitlm in MATLAB to create regression models easily.

Check model output to understand how well it predicts.

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