Interactive Course

Inference for Linear Regression in R

In this course you'll learn how to perform inference using linear models.

4 hours
15 Videos
59 Exercises
6,236 Participants
4,650 XP

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Course Description

Previously, you learned the fundamentals of both statistical inference and linear models; now, the next step is to put them together. This course gives you a chance to think about how different samples can produce different linear models, where your goal is to understand the underlying population model. From the estimated linear model, you will learn how to create interval estimates for the effect size as well as how to determine if the effect is significant. Prediction intervals for the response variable will be contrasted with estimates of the average response. Throughout the course, you'll gain more practice with the dplyr and ggplot2 packages, and you will learn about the broom package for tidying models; all three packages are invaluable in data science.

In the first chapter, you will understand how and why to perform inferential (instead of descriptive only) analysis on a regression model.

In this chapter you will learn about how to use the t-distribution to perform inference in linear regression models. You will also learn about how to create prediction intervals for the response variable.

This chapter covers topics that build on the basic ideas of inference in linear models, including multicollinearity and inference for multiple regression models.

In this chapter you will learn about the ideas of the sampling distribution using simulation methods for regression models.

Additionally, you will consider the technical conditions that are important when using linear models to make claims about a larger population.

1
Inferential ideas
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In the first chapter, you will understand how and why to perform inferential (instead of descriptive only) analysis on a regression model.
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Simulation-based inference for the slope parameter

In this chapter you will learn about the ideas of the sampling distribution using simulation methods for regression models.
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t-Based Inference For the Slope Parameter

In this chapter you will learn about how to use the t-distribution to perform inference in linear regression models. You will also learn about how to create prediction intervals for the response variable.
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Technical Conditions in linear regression

Additionally, you will consider the technical conditions that are important when using linear models to make claims about a larger population.
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Building on Inference in Simple Linear Regression

This chapter covers topics that build on the basic ideas of inference in linear models, including multicollinearity and inference for multiple regression models.
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Jo Hardin

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Jo Hardin is a professor of mathematics and statistics at Pomona College. Her statistical research focuses on developing new robust methods for high throughput data. Recently, she has also worked closely with the statistics education community on ways to integrate data science early into a statistics curriculum. When not working with students or on her research, she loves to put on a pair of running shoes and hit the road.

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Inference for Linear Regression in R

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Course Description

Inferential ideas

Variability in regression lines

Regression output: example I

First random sample, second random sample

Superimpose lines

Research question

Regression hypothesis

Variability of coefficients

Original population - change sample size

Hypothetical population - less variability around the line

Hypothetical population - less variability in x direction

What changes the variability of the coefficients?

t-Based Inference For the Slope Parameter

Mathematical approximation

How do the theoretical results play a role?

t-statistic

Working with R-output (1)

Working with R-output (2)

Comparing randomization inference and t-inference

Intervals in regression

CI using t-theory

Comparing randomization CIs and t-based CIs

Different types of Intervals

Confidence intervals for the average response at specific values

Confidence intervals for the average response for all observations

Prediction intervals for the individual response

Building on Inference in Simple Linear Regression

Inference on transformed variables

Transformed model

Interpreting transformed coefficients

Multicollinearity

LA Homes, multicollinearity (1)

LA Homes, multicollinearity (2)

LA Homes, multicollinearity (3)

Multiple linear regression

Inference on coefficients

Interpreting coefficients

Summary

Simulation-based inference for the slope parameter

Simulation-based Inference

Null sampling distribution of the slope

SE of the slope

p-value

Inference on slope

Simulation-based CI for slope

Bootstrapping the data

SE method - bootstrap CI for slope

Percentile method - bootstrap CI for slope

Inference from randomization and bootstrapped distributions

Technical Conditions in linear regression

Technical conditions for linear regression

Violation of LINE conditions (1)

Violation of LINE conditions (2)

Using residuals (1)

Using residuals (2)

Why do we need the LINE assumptions?

Effect of an outlier

Estimation with and without outlier

Inference with and without outlier (t-test)

Inference with and without outlier (randomization)

Moving forward when model assumptions are violated

Adjusting for non-linear relationship

Adjusting for non-constant errors

Adjusting for non-normal errors