Linear regression (lm) in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the lm() function in R?

The lm() function fits a linear regression model, which finds the best straight line to describe the relationship between a dependent variable and one or more independent variables.

beginner

In the formula lm(y ~ x, data = df), what does y ~ x mean?

It means we want to predict y (dependent variable) using x (independent variable). The tilde ~ separates the outcome from the predictor.

beginner

What does the coefficient estimate in a linear regression model represent?

It shows how much the dependent variable changes when the independent variable increases by one unit, assuming other variables stay the same.

beginner

How do you check the summary of a linear model in R?

Use the summary() function on the model object, like summary(model). It shows coefficients, significance, and model fit statistics.

intermediate

What does the Residuals section in summary(lm) tell you?

It shows the differences between observed and predicted values. Small residuals mean the model fits the data well.

What does the lm() function in R do?

A Fits a linear regression model

B Creates a scatter plot

C Calculates the mean of a variable

D Performs a t-test

The lm() function fits a linear regression model to data.

In lm(y ~ x, data = df), what is y?

A Data frame name

B Dependent variable

C Independent variable

D Model summary

y is the dependent variable we want to predict.

Which function shows detailed results of a linear model in R?

A lm()

B plot()

C mean()

D summary()

summary() shows coefficients, residuals, and statistics of the model.

What does a coefficient estimate of 2 mean in a simple linear regression?

A For each 1 unit increase in x, y increases by 2 units

B The model has 2 predictors

C The residual is 2

D The intercept is 2

Coefficient 2 means y changes by 2 units for every 1 unit increase in x.

What do residuals represent in a linear regression model?

A Model coefficients

B Predicted values only

C Differences between observed and predicted values

D Independent variables

Residuals are the errors or differences between actual and predicted values.

Explain how to fit a simple linear regression model in R using lm() and interpret the output.

Think about predicting one variable from another and checking the model summary.

Describe what residuals are in linear regression and why they matter.

Residuals tell us how well the model predictions match the actual data.

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