Regression analysis in MATLAB - Mini Project: Build & Apply

Regression analysis

📖 Scenario: You are a data analyst at a small company. You have collected data on advertising spending and sales. You want to understand how advertising spending affects sales using regression analysis.

🎯 Goal: Build a simple linear regression model in MATLAB to predict sales based on advertising spending.

📋 What You'll Learn

Create vectors for advertising spending and sales data

Create a variable for the number of data points

Use MATLAB's polyfit function to perform linear regression

Calculate predicted sales using the regression coefficients

Display the regression coefficients and predicted sales

💡 Why This Matters

🌍 Real World

Regression analysis helps businesses understand relationships between variables, like how advertising affects sales.

💼 Career

Data analysts and scientists use regression to make predictions and support decision-making.

1

Create data vectors for advertising spending and sales

Create two vectors called advertising and sales with these exact values: advertising = [5, 10, 15, 20, 25] and sales = [7, 12, 17, 22, 27].

MATLAB

% Your code here

Hint

Use square brackets to create vectors in MATLAB.

2

Create a variable for the number of data points

Create a variable called n that stores the number of elements in the advertising vector using the length function.

MATLAB

advertising = [5, 10, 15, 20, 25];
sales = [7, 12, 17, 22, 27];
% Your code here

Hint

Use length(advertising) to get the number of elements.

3

Perform linear regression using polyfit

Use the polyfit function to find the regression coefficients. Create a variable called coefficients by fitting a first-degree polynomial to advertising and sales.

MATLAB

advertising = [5, 10, 15, 20, 25];
sales = [7, 12, 17, 22, 27];
n = length(advertising);
% Your code here

Hint

Use polyfit(x, y, 1) for linear regression.

4

Calculate predicted sales and display results

Calculate predicted sales using polyval with coefficients and advertising. Store the result in predicted_sales. Then, display coefficients and predicted_sales using disp.

MATLAB

advertising = [5, 10, 15, 20, 25];
sales = [7, 12, 17, 22, 27];
n = length(advertising);
coefficients = polyfit(advertising, sales, 1);
% Your code here

Hint

Use polyval(coefficients, advertising) to get predicted values.

Use disp to show results.

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