We wish to perform a regression analysis to predict Y using X as the independent

Question

We wish to perform a regression analysis to predict Y using X as the independent variable. Use the data given below to find the matrix (X'X)^-1 that would be used in our matrix calculations. (X'X)^-1 = a) [5 5 15 55] b) [4 30 30 75] c) [1.1 -0.3 -0.3 0.1] d) [3.5 -4 -4 1.25] Eleven student teachers took part in an evaluation program designed to measure teacher effectiveness. The response measure was a quantitative evaluation of the teacher. The independent variables were scores on four standardized tests given to each teacher. The model we are trying to fit is: Y = beta_0 + beta_1 X_1 + beta_2 X_2 + beta_3 X_3 + beta_4 X_4 + element Complete the ANOVA table given below for this model: (round solutions to two decimal places where necessary)

Explanation / Answer

X = [1 5 ;1 2 ;1 1 ; 1 3; 1 4];
>> inv(X'*X)

ans =

1.1000 -0.3000
-0.3000 0.1000

hence

option C) is correct

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