# Linear Models (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 3 of 3

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## Question number: 1

» Linear Models » Theory of Linear Estimation » Gauss-Markoff Setup

Appeared in Year: 2014

### Describe in Detail

Define estimability of a linear parametric function in a Gauss Markov model. State and prove a necessary and sufficient condition for estimability.

### Explanation

** Estimability **: The linear parametric function c’β is an estimable function if there exists a vector

a ** R **

^{ n }such that

If X is of full column rank then all linear combinations of β are estimable, since is unique, that is

Suppose we are dealing with the

## Question number: 2

» Linear Models » Analysis of One-Way Classified Data » Mixed Model

Appeared in Year: 2014

### Describe in Detail

A manufacturer of television sets is interested in the effect on tube conductivity of five different types of coating for color picture tubes. Sample means are

Error sum of squares = 54.0

(i) Is there a difference in conductivity due to coating type? F-value = 3.09

(ii) Determine which pair differs significantly using Bonferroni t-interval. Comment on the same.

### Explanation

(i)

Test the null and alternative hypothesis is

H _{0 }: There is no difference in the means of conductivity due to coaching type:

H _{1 }: At least one mean is different from others.

Assume that the testing of hypothesis at 0.05 level of significance.

Given that

## Question number: 3

» Linear Models » Use of G-Inverse

Appeared in Year: 2014

### Describe in Detail

Obtain a g-inverse of A given below and verify that AA ^{-} A = A

### Explanation

Let A be a full rank m n matrix. By full rank we mean rank (A) = min {m, n}.

If m < n, then A has a right inverse given by

If m > n, then A has a left inverse given by

Our matrix A is