Multiple Linear Regression

STAT 20: Introduction to Probability and Statistics

Concept Questions

Today’s questions are centered around a few different linear models made using the data in the penguins data frame.

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

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

m3 <- lm(flipper_length_mm ~ bill_length_mm + bill_depth_mm, 
         data = penguins)

m4 <- lm(flipper_length_mm ~ bill_length_mm + 
  bill_depth_mm + species, 
         data = penguins)

Question 1

01:00

m1

Call:
lm(formula = flipper_length_mm ~ bill_length_mm, data = penguins)

Coefficients:
   (Intercept)  bill_length_mm  
       127.330           1.674  

Which is the correct interpretation of the coefficient in front of bill length?

This assesses students’ ability to interpret a slope coefficient in simple linear regression based on how their values impact the estimated y variable.

Question 2

01:00

m2

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

Coefficients:
     (Intercept)    bill_length_mm  speciesChinstrap     speciesGentoo  
         147.563             1.096            -5.247            17.552  

Which is the correct interpretation of the coefficient in front of bill length?

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

Question 3

01:00

m2

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

Coefficients:
     (Intercept)    bill_length_mm  speciesChinstrap     speciesGentoo  
         147.563             1.096            -5.247            17.552  

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

This one assesses their ability to interpret an indicator varaible coefficient.

The most common interpretation should involve a comparison to the reference level (Adelie) and will mention that we need to fix the value of the other, numerical variable in the model.

Question 4

01:00

m3

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

Coefficients:
   (Intercept)  bill_length_mm   bill_depth_mm  
       194.218           1.409          -3.218  

Which is the correct interpretation of the coefficient in front of bill length?

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

Question 5

01:00

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

m4 <- lm(flipper_length_mm ~ bill_length_mm + 
  bill_depth_mm + species, 
         data = penguins)

How many more coefficients does the model m4 have than m1?

m4 has one more numerical variable than m1, and one more categorical variable as well. This adds 1 more coefficient and 2 more coefficients (there are three penguin species, so 3-1), respectively. The correct answer should be three more coefficients.

Problem Set: Multiple Linear Regression

20:00

Break

05:00

Lab: Flights II

25:00