Design Matrices For Linear Models, Clearly Explained!!! 

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As a pure mathematician who studied a fair bit of design theory i find the use of designs in statistics fascinating

First of all, your videos are the best thing that exists on the internet. I just bought your linear regression study guide. Secondly, if I were expecting the slope for the line between the control and mutant mice to have different slopes could I create a fourth column in my matrix. The third column would have the x values for the control mice in the first four rows and and then zeros in the last four rows. The fourth column would have zeros in the first four rows and then the x values for the mutant mice in the last four rows. In my equation I would have the slope for the control mice multiplied by column three plus the slope for the mutant mice multiplied by column four. Then when I calculate my F value my parameters for that equation (p-fancy) would be 4 and I could calculate if it fits better than any simpler version. In my data I am working with a situation like this and I would like to know if this all is valid.

Amazing content, thank you so much Josh 🙌

God this is so useful and just saved my module! Thank you so much. Oh I love StatQuest.

Thanks

I tend not to introduce it that way. When i begin with the linear regression, i introduce with dummy variables and them I make them notice that the ANOVA is just a specific case of linear regression with those dummy variables and that the test is just a partial Fisher test. I hope that you will explain contrasts as they often generate error among students

I think something is slightly blurry in the explanation for those (me) coming to this with hypothesis testing, rather than models, centered in the mind: You're not completely explicit why you want to compare different/simpler models, and if/why this constitutes the basis of a hypothesis test. How does this sound?: To test if the measured weight* is significantly different between mouse genotypes, one starts by constructing a comprehensive glm (of multiple parameters, if necessary) to predict the measured weight. Then by applying the F = ... equation, you compare the fit of this first glm, with another one which specifically leaves out the parameter of interest, mouse genotype, but includes all the other parameters. This thereby isolates the influence of the genotype parameter in predicting mouse weight. * I guess in this example it's actually weight relative to size..

StatQuest could you please number all your fantastic videos so it would be easier to find their order in your series of lectures? E.g now I have a hard time to find your first video "GLM PART 1" on this series on "GLMs"

Hey Josh, amazing content, I wanted request you to create a statquest on K-mer counting and NLP. Thanks

Brilliant as usual! I'm just wondering, when comparing the two regression lines, how you would deal with the design matrix in case the slope is different for normal and mutant mice. Would it be acceptable to split the third column into two, with 0 and non-zero values to "turn on and off" the slope corresponding to each type?

I'm a beginner. Your explanation is surprisingly clear. But I am confused because the dummy variable coding and design matrices look very similar. Can you tell what the difference is if possible?

hey josh! thx a bunch for this awesume video! a question to the last example (batch effect): is this basically what is considered to be the interaction term in the multifactorial anova? PS: i love the illustrated guide to machine learning! keep up the good work and make more of these please!