In fitting a SLR model, ten of the residuals for the regression of weight on age
ID: 3177984 • Letter: I
Question
In fitting a SLR model, ten of the residuals for the regression of weight on age for eleven children are: 0.02, -0.02, 0.01, -0.01, -0.04, 0.03, 0.01, 0.02, 0.01, 0.05 What is the eleventh residual? Consider the multiple regression model: Y_i = P_i X_i1 + beta_2 X_i2 + element_i, i = 1..., n, where the element_i are uncorrelated, with E(element_i) = 0 and Var(element_i) = sigma^2. Let X = (X_11 X_21 X__n1) and X^T X is invertible (i.e., full rank). Write the normal equations using the least square criterion. What are the least square estimators of beta_1 and beta_2? Let e_i denote the residual and Y_i the fitted value for i = 1, ..., n. Which of the following statements are true? sigma n i = 1 e_i = 0 always. sigma n i = 1 e_Yi = 0 always. sigma n i = 1 Y_i always for j = 1, 2. sigma n i = 1 Y_i = 0 always.Explanation / Answer
Problem 2:
let e11 denote the eleventh residual.then,
0=sum of residuals=0.02+(-0.02)+0.01+(-0.01)+(-0.04)+0.03+0.01+002+0.01+0.05+e11
=0.08+e11
Thus e11=-0.08
The eleventh residual is -0.08