2017 Statistics Paper - II

The following ANOVA table is obtained for a two-variable linear regression : The correlation between the regressor and the regressand is [IMAGE]

In a 2-way ANOVA with 6 rows, 5 columns and 3 observations per cell, what are the degrees of freedom for the sum of squares for interaction and error respectively?

If Y1, Y2, Y3 and Y4 are independent with E(Y1) = E(Y2) = 1 + 2 E(Y3) = E(Y4) = 1 + 3 Var(Yi) = 2; i = 1, 2, 3, 4 the condition of estimability of the parametric function l11 + l22 + l33 is

Let yi follow N( + xi, 2); i = 1, 2, 3, ..., n Let (0, 1) and (0, 1) be the least squares and maximum likelihood estimates of (, ) respectively. Then which one of the following is correct?

In a multiple linear regression model with 5 regressors and 25 observations, the sum of squares due to regressors was 360 and the sum of squares due to errors was 128. For this model, consider the following statements : 1. Almost 74% of the total variation in the model is explained by the regressors. 2. The estimated value of the error variance of the model is 3 .2. Which of the above statements is/are correct?

In the following, the Gauss-Markov model is stated as Y = Xβ + ε and X- denotes the g-inverse of the matrix X : 1. XX- X = X 2. If X is non-singular, then X- = X-1 3. X- is needed when the columns of X are linearly dependent Which of the above is/are correct?