Multiple Linear Regression

STAT 20: Introduction to Probability and Statistics

Concept Questions

Question 1

m1 <- lm(bill_depth_mm ~ bill_length_mm, data = penguins)

m2 <- lm(bill_depth_mm ~ bill_length_mm + body_mass_g + species, 
         data = penguins)

How many more coefficients does the second model have than the first?

Remind students that they need to remember whether species and body_mass_g are numerical or categorical. Students should know how many species there are (three).

One addl. coefficient for body mass; two addl. for species (one less than the number of species, which is three). This gives a total of three more coefficients.

Questions 2-4

Consider the following multiple linear regression model, which will be the subject of the next three review questions.

Question 2

01:00

m2

Call:
lm(formula = bill_depth_mm ~ bill_length_mm + body_mass_g + species, 
    data = penguins)

Coefficients:
     (Intercept)    bill_length_mm       body_mass_g  speciesChinstrap  
        10.33083           0.09484           0.00117          -0.90748  
   speciesGentoo  
        -5.80117  

Which is the correct interpretation of the coefficient in front of bill length? Select all that apply.

This one assesses their ability to use a conditional interpretation of a regression coefficient (controlling for the other variables in the model…).

The correct interpretation controls for both other variables (body mass and species), and has the x variable and the y variable in the correct places.

Question 3

01:00

m2

Call:
lm(formula = bill_depth_mm ~ bill_length_mm + body_mass_g + species, 
    data = penguins)

Coefficients:
     (Intercept)    bill_length_mm       body_mass_g  speciesChinstrap  
        10.33083           0.09484           0.00117          -0.90748  
   speciesGentoo  
        -5.80117  

Which is the correct interpretation of the coefficient in front of Gentoo?

This one assesses their ability to use a conditional interpretation of a regression coefficient (controlling for the other variables in the model…)

The correct interpretation needs to involve a comparison to the reference level, Adelie and should not involve anything about bill length or body mass, (other than to say they should be fixed).

Question 4

01:00

m2

Call:
lm(formula = bill_depth_mm ~ bill_length_mm + body_mass_g + species, 
    data = penguins)

Coefficients:
     (Intercept)    bill_length_mm       body_mass_g  speciesChinstrap  
        10.33083           0.09484           0.00117          -0.90748  
   speciesGentoo  
        -5.80117  

How would this linear model best be visualized?

Three numerical variables means we will have planes in a 3D space. The coefficients for the dummy variables will shift the planes up and down. There are three species, so three parallel planes is what we are looking for.

Problem Set: Multiple Linear Regression

20:00

Break

05:00

Lab: Flights II

25:00