Matrices and vectors will play an important role for us in linear regression. Let's review some...

 

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Matrices and vectors will play an important role for us in linear regression. Let's review some matrix theory as it might relate to linear regression. Consider the system of linear equations Y₁ = Bo + +8, ² BjZij + Eir j=1 for i = 1,..., n, where n is the number of data points (measurements in the sample), and j = 1,...,p, where 1. p + 1 is the number of parameters in the model. 2. Y₂ is the ith measurement of the response variable. 3. is the ith measurement of the 5th predictor variable. 4. & is the 7th error term and is a random variable, often assumed to be N(0,0²). 5. Bj, j = 0,...,p are unknown parameters of the model. We hope to estimate these, which would help us characterize the relationship between the predictors and response. A.2.(a) [5 points] Write the equation above in matrix vector form. Call the matrix including the predictors X, the vector of Y₂s Y, the vector of parameters B, and the vector of error terms €. (This is more LaTeX practice than anything else...) Matrices and vectors will play an important role for us in linear regression. Let's review some matrix theory as it might relate to linear regression. Consider the system of linear equations Y₁ = Bo + +8, ² BjZij + Eir j=1 for i = 1,..., n, where n is the number of data points (measurements in the sample), and j = 1,...,p, where 1. p + 1 is the number of parameters in the model. 2. Y₂ is the ith measurement of the response variable. 3. is the ith measurement of the 5th predictor variable. 4. & is the 7th error term and is a random variable, often assumed to be N(0,0²). 5. Bj, j = 0,...,p are unknown parameters of the model. We hope to estimate these, which would help us characterize the relationship between the predictors and response. A.2.(a) [5 points] Write the equation above in matrix vector form. Call the matrix including the predictors X, the vector of Y₂s Y, the vector of parameters B, and the vector of error terms €. (This is more LaTeX practice than anything else...)