Linear regression (lm) in R Programming - Mini Project: Build & Apply

Simple Linear Regression with lm in R

📖 Scenario: You are a data analyst at a small company. You want to understand how advertising spending affects sales. You have data on advertising budgets and sales for several months.

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

📋 What You'll Learn

Create a data frame with advertising and sales data

Create a variable for the formula to use in the model

Use the lm function to build the linear regression model

Print the summary of the model to see the results

💡 Why This Matters

🌍 Real World

Linear regression is used in business to understand relationships between variables, like advertising spend and sales.

💼 Career

Data analysts and data scientists use linear regression to build predictive models and make data-driven decisions.

1

Create the data frame

Create a data frame called ad_data with two columns: advertising and sales. Use these exact values: advertising = c(10, 20, 30, 40, 50), sales = c(15, 25, 35, 45, 55).

R Programming

# Create the data frame ad_data with advertising and sales columns
# Your code here

Hint

Use data.frame() to create the data frame with the exact column names and values.

2

Create the formula variable

Create a variable called model_formula that stores the formula sales ~ advertising.

R Programming

ad_data <- data.frame(advertising = c(10, 20, 30, 40, 50), sales = c(15, 25, 35, 45, 55))
# Create the model_formula variable with sales ~ advertising
# Your code here

Hint

Use the tilde ~ to create the formula for the model.

3

Build the linear regression model

Use the lm function to create a linear model called model using model_formula and the data frame ad_data.

R Programming

ad_data <- data.frame(advertising = c(10, 20, 30, 40, 50), sales = c(15, 25, 35, 45, 55))
model_formula <- sales ~ advertising
# Create the linear model called model using lm()
# Your code here

Hint

Use lm(formula, data = ...) to build the model.

4

Print the model summary

Print the summary of the linear model model using the summary() function.

R Programming

ad_data <- data.frame(advertising = c(10, 20, 30, 40, 50), sales = c(15, 25, 35, 45, 55))
model_formula <- sales ~ advertising
model <- lm(model_formula, data = ad_data)
# Print the summary of the model
# Your code here

Hint

Use print(summary(model)) to see the details of the regression.

Practice

1. What does the lm() function in R do?

easy

A. Fits a linear regression model to predict a variable

B. Creates a plot of data points

C. Calculates the mean of a numeric vector

D. Performs a t-test between two groups

Solution

1. Step 1: Understand the purpose of lm() and compare options

   The lm() function is used to fit linear models, which means it finds a line that best predicts one variable from others. Options A, B, and D describe other functions or analyses, not linear regression modeling.

2. Final Answer:

   Fits a linear regression model to predict a variable -> Option A

3. Quick Check:

   lm() fits linear regression [OK]

Hint: Remember: lm() stands for linear model fitting [OK]

Common Mistakes:

• Confusing lm() with plotting functions
• Thinking lm() calculates summary statistics only
• Mixing lm() with hypothesis testing functions

2. Which of the following is the correct syntax to fit a linear model predicting y from x in R?

easy

A. model <- lm(y ~ x, data = mydata)

B. model <- lm(x ~ y, data = mydata)

C. model <- lm(y, x, data = mydata)

D. model <- lm(data = mydata, y = x)

Solution

1. Step 1: Recall the formula syntax for lm() and check options

   The correct syntax uses lm(response ~ predictor, data = dataset). Here, y is the response and x the predictor. model <- lm(y ~ x, data = mydata) matches. model <- lm(x ~ y, data = mydata) reverses response and predictor. model <- lm(y, x, data = mydata) uses wrong argument order. model <- lm(data = mydata, y = x) uses = instead of ~.

2. Final Answer:

   model <- lm(y ~ x, data = mydata) -> Option A

3. Quick Check:

   lm(response ~ predictor, data) [OK]

Hint: Formula is always response ~ predictor in lm() [OK]

Common Mistakes:

• Swapping response and predictor variables
• Passing variables without formula syntax
• Misordering arguments in lm()

3. What will be the output of this R code?

data <- data.frame(x = 1:5, y = c(2, 4, 6, 8, 10))
model <- lm(y ~ x, data = data)
coef(model)

medium

A. Intercept = 0, Slope = 1

B. Intercept = 2, Slope = 1

C. Intercept = 1, Slope = 2

D. Intercept = 0, Slope = 2

Solution

1. Step 1: Analyze data and model fit

   The data has x = 1 to 5 and y = 2,4,6,8,10 which is exactly y = 2*x. Since y = 2*x perfectly, intercept is 0 and slope is 2.

2. Final Answer:

   Intercept = 0, Slope = 2 -> Option D

3. Quick Check:

   y = 2*x means intercept 0, slope 2 [OK]

Hint: Check if y is exactly a multiple of x for slope [OK]

Common Mistakes:

• Assuming intercept is 1 by default
• Mixing up slope and intercept values
• Not checking data pattern before fitting

4. Identify the error in this R code for linear regression:

data <- data.frame(x = 1:4, y = c(3, 6, 9, 12))
model <- lm(y = x, data = data)
summary(model)

medium

A. Missing library call for lm()

B. Incorrect formula syntax in lm()

C. summary() cannot be used on lm objects

D. Data frame creation is wrong

Solution

1. Step 1: Check lm() call and verify other code

   The lm() function requires a formula like response ~ predictor. Here, y = x is incorrect syntax. Data frame creation is correct. summary() works on lm objects. lm() is base R, no library needed.

2. Final Answer:

   Incorrect formula syntax in lm() -> Option B

3. Quick Check:

   lm() needs formula, not y = x [OK]

Hint: lm() needs formula like y ~ x, not y = x [OK]

Common Mistakes:

• Using = instead of ~ in lm() formula
• Assuming summary() is not for lm objects
• Thinking lm() requires extra libraries

5. You have a dataset with variables height and weight. You want to predict weight from height using linear regression. After fitting model <- lm(weight ~ height, data = df), the summary shows a very low R-squared value. What is the best next step?

hard

A. Remove the intercept term to force a better fit

B. Use the model as is because R-squared is not important

C. Try adding more predictor variables to improve the model

D. Switch to a t-test instead of regression

Solution

1. Step 1: Interpret low R-squared and next steps

   A low R-squared means the model explains little of the variation in weight using height alone. Adding more predictors can help explain more variation. Removing intercept or ignoring R-squared is not good practice. A t-test is unrelated.

2. Final Answer:

   Try adding more predictor variables to improve the model -> Option C

3. Quick Check:

   Low R-squared? Add predictors [OK]

Hint: Low R-squared? Add more predictors to improve [OK]

Common Mistakes:

• Removing intercept to fix low R-squared
• Ignoring model fit quality
• Confusing regression with hypothesis testing