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  3. Inference for Linear Regression in R
  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

Initializing

Exercise

CI using t-theory

In previous courses, you have created confidence intervals with the formula of statistic plus/minus some number of standard errors. With bootstrapping, we typically use two standard errors. With t-based theory, we use the specific t-multiplier.

Create a CI for the slope parameter using both the default tidy() call as well as mutate() to calculate the confidence interval bounds explicitly. Note that the two methods should give exactly the same CI values because they are using the same computations.

alpha has been set to 0.05 and the degrees of freedom of the twins dataset is given to you.

Instructions 1/2

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  • Calculate the confidence level as one minus alpha.
  • Calculate the upper percentile cutoff from alpha.
  • Calculate the critical value from the inverse cumulative density function of the t-distribution, qt(). Pass it the upper percentile cutoff and the degrees of freedom.