Hello! I am stuck on how to interpret or deduce design matrices for regression analysis. I was wondering if you could answer this question, but also provide a bit of background on how they work.

This question in particular deals with a model that has two explanatory variables and one of them is quadratic. Throughout the process of deriving the model using calculus, a design matrix is used - why is this the case?

I've included a few question which I was unable to answer which I was hoping you could help with :)

Exercise: With IA) = (60,331, . . .,bp)T, check that you can follow the same steps with p = 3 explanatory variables and general p 2 2, and get (3.17) (2313 = 11%, where y is the same as in the middle of (3.9), 1 I11 31p 1 9321 32;: ED 3 E " . E A 51 (3.18) X = 1 mil - - - Iip 3 b = E 2 32 1 mm 3m: The dimensions are: (3.19) dim (X) = (3.20) dim (KT) = (3.21) dim (XTX) = (3.22) dim (XTy) = (3.23) dim (13) = II For terminology1 X is sometinles referred to as the design matrix or data matrix, especially in experinlents where the investigator has control over choosing values of explanatory variables before observing 3;. Equation (3.17) is called the system of normal equations. The numerically stable way to solve it is through the QR decomposition (check components of the lsfit or In objects in R)