Question:Which of the following statements are associated with residuals of a regression model? The sum of the residuals in any regression model that contains an intercept is always zero. The sum of the observed values yiy_iyi​ is not equal to the sum of the fitted values y^i\hat{y}_iy^​i​. The sum of the residuals weighted by the corresponding regressor variable is zero. The sum of the residuals weighted by the corresponding fitted values is zero. Select the c

Question What are Western Disturbances and Westerlies, and how are they different from monsoons? In which part of India are they mainly confined? ISS PREVIOUS YEAR GS 2016 Q.NO. 2(b)

One of the most common questions students ask while preparing for government exams is: “How many hours should I study every day?” Many students feel that they need to study 12–14 hours daily to succeed. But the truth is a little different.

Let the random variable X have the distribution: P(X = 0) = P(X = 3) = p P(X = 1) = 1 − 3p P(X = 2) = p where 0 ≤ p ≤ 1/2 Find the maximum value of V(X).

Which of the following statements are correct about the generalized inverse of a matrix A? A generalized inverse of a matrix is defined as A A⁻ A = A A generalized inverse is not unique. A matrix to have a generalized inverse must be non-singular. A matrix to have a generalized inverse may be either a square matrix or a rectangular matrix. Select the correct answer using the code given below:

What is Polar Shifting? Discuss its geographic significance with regard to catastrophic consequences on humanity.

Government exams in India are highly competitive. Every year, lakhs of students apply for various exams such as banking, SSC, railways, teaching services, and statistical services. While many students work hard, only a small percentage achieve success.

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A  Random Effects Model Question (ISS Level)  Question Suppose b₁, b₂, b₃, …, bₙ are independent N(0, σ²) random variables and eᵢⱼ are independent N(0, τ²) random variables for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Suppose we observe only: Xᵢⱼ = bᵢ + eᵢⱼ for i = 1, 2, 3, …, k and j = 1, 2, 3, …, n. Then which of the following assertions are true? Var(Xᵢⱼ) = σ² + τ² for all i, j Cov(Xᵢ

It is absolutely possible to crack the competitive exam in the first attempt with the proper strategy, hard work, and guidance. The proper understanding of the syllabus, concepts, and proper discipline are the major factors of success.

If you are really interested in making your career in statistics and serving your nation, then proper guidance can definitely do wonders for you. Here in this article, we will discuss how you can prepare for your ISS exam in an effective way and how Sunrise Classes in Delhi can help you achieve your dream

A Poisson random variable X has mean equal to 1/2. Let Y = 2X. Consider the following: E(Y) = 1 Var(Y) = 4 μ3(Y) = 4 μ4(Y) = 28 Which of the above is/are correct?

Prepare for Indian Statistical Service (ISS) Exam 2026 with expert guidance from Sunrise Classes. Get study material, mentorship, and test series for ISS success.

ISS PREVIOUS YEAR GS 2016 Q.NO. 5 What does Yoga represent in Indian philosophical tradition? Is it the same as that practised by the masses in the present day?

In the Gauss-Markov linear model, letŷ denote the vector of fitted values andê denote the vector of residuals. Consider the following statements: The components of ŷ are pairwise uncorrelated. The components of ê are pairwise uncorrelated.

For the distribution: f(x) = [1 / B(p, q)] × [x^(p − 1) / (1 + x)^(p + q)],where 0 < x < ∞, p > 0, q > 0, find the harmonic mean. Options: (a) p / (p + q) (b) 1 / p (c) (p − 1) / q (d) (p + 1) / (q − 1)

The Indian Statistical Service (ISS) exam is a highly specialized and competitive examination that demands strong conceptual clarity and consistent practice. Many aspirants often ask: “How should I study daily?” “What routine should I follow to crack ISS?”

The division of India into provinces and the evolution of a system of provincial administration by Akbar was an effective system of governance. Comment.

ISS PREVIOUS YEAR PAPER-1 2016 SOLUTION. The following data pertain to a test involving analysis of variance: Estimate of population variance based on variance among the sample means = 18.50. Estimate of the population variance based on the variance within the samples = 12.50 The F-ratio for the sample is equal to: Options:(a) 0.68(b) 1.48(c) 6.00(d) 31.00

X₁ and X₂ are independent Poisson random variables such that: P(X₁ = 2) = P(X₁ = 1)P(X₂ = 2) = P(X₂ = 3) Find the variance of (X₁ − 2X₂).

A certain task can be accomplished in a factory by four different workers on five different types of machines. A sample study in context of a two-way design without repeated value is being made with two fold objectives of examining whether the four workers differ with respect to mean productivity and whether it is same for five machines. The researcher involved in this study reports gathered data as under : Sum of squares for variance between machines = 35.2 Sum of squares