Lab 02
Linear regression
January 24, 2025
Welcome
Goals
- LaTex in this course
- Lab 02: Linear regression
LaTex in this class
For this class you will need to be able to…
Properly write mathematical symbols, e.g., \(\beta_1\) not B1, \(R^2\) not R2
Write basic regression equations, e.g., \(\hat{y} = \beta_0 + \beta_1x_1 + \beta_2x_2\)
Write matrix equations: \(\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}\)
Write hypotheses (we’ll start this next week), e.g., \(H_0: \beta = 0\)
You are welcome to but not required to write math proofs using LaTex.
Writing LaTex
Inline: Your mathematics will display within the line of text.
Use
$to start and end your LaTex syntax. You can also use the menu: Insert -> LaTex Math -> Inline Math.Example: The text
The linear regression model is $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}$producesThe linear regression model is \(\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}\)
Writing LaTex
Display: Your mathematics will display outside the line of text
Use a
$$to start and end your LaTex syntax. You can also use the menu: Insert -> LaTex Math -> Display Math.Example: The text
The estimated regression equation is $$\hat{\mathbf{y}} = \mathbf{X}\hat{\boldsymbol{\beta}}$$producesThe estimated regression equation is
\[ \hat{\mathbf{y}} = \mathbf{X}\hat{\boldsymbol{\beta}} \]
Tip
Click here for a quick reference of LaTex code.
Describing bivariate relationships
Describe the relationship between the price and width of Ikea sofas, armchairs, and bookcases/shelving.
Lab 02: Linear regression
Today’s lab focuses on using simple and multiple linear regression to understand variability in coffee quality ratings.
