Finish SLR + Introduce MLR

Lecture 15

Dr. Elijah Meyer

Duke University
STA 199 - Fall 2023

2023-10-19

Checklist

– Welcome Back :)

– Clone ae-14

– hw-5 released Tuesday Oct 24

– Lab next week: Project Proposal

Goals

– Finish SLR

– Introduce MLR

– Interpret coefficients

– Introduce the difference between additive and interaction models

Warm Up 1

– What is the difference between simple linear regression and multiple linear regression?

Warm Up 2

Interpret the slope coefficient in the context of the problem

library(tidyverse)
library(tidymodels)
library(palmerpenguins)

linear_reg() |>
  set_engine("lm") |>
  fit(body_mass_g ~ flipper_length_mm , data = penguins) |>
  tidy()

# A tibble: 2 × 5
  term              estimate std.error statistic   p.value
  <chr>                <dbl>     <dbl>     <dbl>     <dbl>
1 (Intercept)        -5781.     306.       -18.9 5.59e- 55
2 flipper_length_mm     49.7      1.52      32.7 4.37e-107

Warm Up 3 (Together)

Write our the estimated equation using proper notation.

Interpret the coefficient associated with the Dream island.

library(tidyverse)
library(tidymodels)
library(palmerpenguins)

linear_reg() |>
  set_engine("lm") |>
  fit(body_mass_g ~ island, data = penguins) |>
  tidy()

# A tibble: 3 × 5
  term            estimate std.error statistic   p.value
  <chr>              <dbl>     <dbl>     <dbl>     <dbl>
1 (Intercept)        4716.      48.5      97.3 8.93e-250
2 islandDream       -1003.      74.2     -13.5 1.42e- 33
3 islandTorgersen   -1010.     100.      -10.1 4.66e- 21

Multiple Linear Regression

What happens if we want to include information from more than one variable to better explain our response?

– ae-14

— \(R^2\) review

— Fitting MLR models in R