Intro to linear regression

The total length of the videos in this section is approximately 31 minutes. Feel free to do this in multiple sittings! You will also spend time answering short questions while completing this section.

You can also view all the videos in this section at the YouTube playlist linked here.

Possible models for the Mean of Y, given X

(There is a written typo at 8:03 in the video below. I write that the linearity assumption of a linear regression is "usually true," but that's not true. What I meant is what I actually said in the audio, which is that the assumption is usually not true.)

Question 1: Does the linearity assumption hold for the picture and the equation at the end of the video?

The answer is at the beginning of the next video.

Linearity and independence assumptions

Question 2: Do you think that the independence assumption holds for the picture in the video?

The answer is at the beginning of the next video.

Normality assumption

Question 3: Do you think that regression is robust to its normality assumption?

The answer is at the beginning of the next video.

Equal variance assumption (aka, homoskedasticity)

Question 4: Linear regression is a generalization of the

• pooled t-test

• unpooled t-test

Putting it all together

Question 5: What symbol do we use for the variance of the y values within each subgroup based on X?

And that is all.

During this tutorial you learned:

• About considering an equal means model v. a separate means model v. any linear regression model

• The assumptions underlying the linear regression model

• The definition of residual

• The notation of the linear regression model 

Terms and concepts:

linear regression model, equal means model, separate means model, linearity, independence within, independence between, residual, normality of residuals, equal variance assumption/homoskedasticity