Multiple Predictors

Lecture 18

Dr. Elijah Meyer + Konnie Huang

Duke University
STA 199 - Fall 2022

October 31st, 2022

Checklist

– Clone ae-17

– If you do not have ae-17 go here: https://github.com/sta199-f22-2/ae-17

Announcements

– Lab Feedback (Check it regardless of your grade)

– HW4 Question 2

Goals

– Overfitting

– “New” function in R

Summary on Regression

– Why we model data?

– Can I write out models?

– Can I interpret model output?

– Do I understand the difference between models?

Warm Up

Discuss the difference between the two models below. Which model would you prefer to fit to model these data? Why?

Overfitting

– Overfitting is a concept in data science, which occurs when a statistical model fits exactly against its data.

– This doesn’t make sense if are goal is to predict!

Why we use regression

• Predict the value of our response

• Estimate the effect of some explanatory variable on the response (examine the relationship)

• Make inference about some larger population (coming later)

When and why we use regression

• Quantitative Response

• Does it make sense

Extension (Coming Later)

To test hypotheses and make conclusions, certain assumptions need to be met….

– Normality of Residuals

– Linearity

– Independence

– Constant Variance

Jump into ae-17

Adjusted R-squared

Modeling More Than One Variable

– Multiple linear regression is used to estimate the relationship between two or more explanatory variables and one response variable.

– we want to predict the value of a variable based on the value of two or more other variables

– “account for X1 and assess the relationship between X2 and Y” - main effects

– “does X1’s relationship with Y change based on X2”

Logistic Regression

– What if the response variable is categorical?