STA 221 - Spring 2025

Goals

For this class you will need to be able to…

Properly write mathematical symbols, e.g., $β_{1}$ not B1, $R^{2}$ not R2
Write basic regression equations, e.g., $\hat{y} = β_{0} + β_{1} x_{1} + β_{2} x_{2}$
Write matrix equations: $y = X β + ϵ$
Write hypotheses (we’ll start this next week), e.g., $H_{0} : β = 0$

You are welcome to but not required to write math proofs using 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 $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}$ produces

The linear regression model is $y = X β + ϵ$

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}}$$ produces

The estimated regression equation is

$\hat{y} = X \hat{β}$

Tip

Click here for a quick reference of LaTex code.

Describe the relationship between the price and width of Ikea sofas, armchairs, and bookcases/shelving.

Today’s lab focuses on using simple and multiple linear regression to understand variability in coffee quality ratings.