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Inference for Linear Regression in R

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

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4 Hours15 Videos59 Exercises11,667 Learners4650 XPStatistical Inference with R Track

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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.
  1. 1

    Inferential ideas

    Free

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

    Play Chapter Now
    Variability in regression lines
    50 xp
    Regression output: example I
    100 xp
    First random sample, second random sample
    100 xp
    Superimpose lines
    100 xp
    Research question
    50 xp
    Regression hypothesis
    50 xp
    Variability of coefficients
    50 xp
    Original population - change sample size
    100 xp
    Hypothetical population - less variability around the line
    100 xp
    Hypothetical population - less variability in x direction
    100 xp
    What changes the variability of the coefficients?
    50 xp
  2. 2

    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.

    Play Chapter Now
    Simulation-based Inference
    50 xp
    Null sampling distribution of the slope
    100 xp
    SE of the slope
    100 xp
    p-value
    100 xp
    Inference on slope
    50 xp
    Simulation-based CI for slope
    50 xp
    Bootstrapping the data
    100 xp
    SE method - bootstrap CI for slope
    100 xp
    Percentile method - bootstrap CI for slope
    100 xp
    Inference from randomization and bootstrapped distributions
    50 xp
  3. 3

    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.

    Play Chapter Now
    Mathematical approximation
    50 xp
    How do the theoretical results play a role?
    50 xp
    t-statistic
    100 xp
    Working with R-output (1)
    100 xp
    Working with R-output (2)
    100 xp
    Comparing randomization inference and t-inference
    100 xp
    Intervals in regression
    50 xp
    CI using t-theory
    100 xp
    Comparing randomization CIs and t-based CIs
    100 xp
    Different types of intervals
    50 xp
    Confidence intervals for the average response at specific values
    100 xp
    Confidence intervals for the average response for all observations
    100 xp
    Prediction intervals for the individual response
    100 xp
  4. 4

    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.

    Play Chapter Now
    Technical conditions for linear regression
    50 xp
    Violation of LINE conditions (1)
    50 xp
    Violation of LINE conditions (2)
    50 xp
    Using residuals (1)
    100 xp
    Using residuals (2)
    100 xp
    Why do we need the LINE assumptions?
    50 xp
    Effect of an outlier
    50 xp
    Estimation with and without outlier
    100 xp
    Inference with and without outlier (t-test)
    100 xp
    Inference with and without outlier (randomization)
    100 xp
    Moving forward when model assumptions are violated
    50 xp
    Adjusting for non-linear relationship
    100 xp
    Adjusting for non-constant errors
    100 xp
    Adjusting for non-normal errors
    100 xp
  5. 5

    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.

    Play Chapter Now
    Inference on transformed variables
    50 xp
    Transformed model
    100 xp
    Interpreting transformed coefficients
    50 xp
    Multicollinearity
    50 xp
    LA Homes, multicollinearity (1)
    100 xp
    LA Homes, multicollinearity (2)
    100 xp
    LA Homes, multicollinearity (3)
    100 xp
    Multiple linear regression
    50 xp
    Inference on coefficients
    100 xp
    Interpreting coefficients
    50 xp
    Summary
    50 xp

In the following tracks

Statistical Inference with R

Datasets

LA home price dataNYC restaurant dataTwin data

Collaborators

Nick Carchedi
Nick Solomon

Prerequisites

Foundations of Inference in RIntermediate Regression in R
Jo Hardin Headshot

Jo Hardin

Professor at Pomona College

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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