202405202250
Status: #idea
Tags: Hypothesis Testing in Multiple Linear Regression

Test on Significance of Model (Crucial to know, but in general we know that our model is significant.)

We use Analysis of Variance (ANOVA) to check the significance of our regression model.
Analysis of Variance (ANOVA) in the context of Multiple Linear Regression will check if there is any linear relationship between the response and any of the regressor variables.

In other words it checks the following
$H_0:{\beta }_1=\cdots ={\beta }_k=0$
$H_1:\text{at least one of the cited coefficients has a positive slope}$
equivalently
$H_1:{\beta }_j\ne 0\text{, for some}j\ne j$

We're literally just doing Analysis of Variance (ANOVA), so like in it we reject if our null hypothesis if our $F$ statistic is bigger than the $F_{\alpha }$ statistic for a given confidence level $\alpha$.

*Read the following screen capture and make sure you understand it, this contains everything you need to know

Relevant Links

Video from Which The Screencaps Originate