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Course

Inference for Linear Regression in R

AdvancedSkill Level

4.8+

Updated 12/2021

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

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RProbability & Statistics4 hours15 videos59 Exercises4,650 XP14,686Statement of Accomplishment

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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.

Prerequisites

Foundations of Inference in R Intermediate Regression in R

1

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?

2

Simulation-based inference for the slope parameter

Simulation-based Inference

Null sampling distribution of the slope

SE of the slope

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

3

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

4

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

5

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

Inference for Linear Regression in R

Course
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*4.8

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Sort by

Vitalii

10 days

Thi Thu Ha

16 days

Clear explanations and well-structured exercises. Helped me understand confidence intervals, hypothesis testing, and model assumptions in linear regression. Great for beginners and intermediate learners

SANDRA

22 days

ΑΝΔΡΕΑΣ

about 1 month

Great course for regression models

Irvin Sinué

about 1 month

ERNESTO

about 1 month

Excellent course of R inference

Vitalii

"Clear explanations and well-structured exercises. Helped me understand confidence intervals, hypothesis testing, and model assumptions in linear regression. Great for beginners and intermediate learners"

Thi Thu Ha

SANDRA

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