Question 1

In the case of a two-variable regression model show that TSS = ESS + RSS. Use appropriate diagram to explain your result. In this context, define the concept of R-squared and interpret it.

Accepted Answer

In a two-variable regression model, the total variation in the dependent variable (Y) can be decomposed into two parts: the variation explained by the regression model and the variation unexplained by it. This fundamental decomposition is expressed by the identity: TSS = ESS + RSS.

This identity is derived from the basic relationship between an observed value, its mean, and its predicted value. For any observation Yᵢ, we can express its deviation from the mean (Ȳ) as the sum of its deviation f

Question 2

The relationship between Y and X is given by yi =x +ẞxi + u¡ where u¡ follows classical assumptions. Consider the following set of data and answer the questions. Y 11 12 13 14 15 X 18 16 19 22 20

Accepted Answer

Answer available — download the full PDF for complete details.

Question 3

Explain the concept of identification in a simultaneous equations model. Why is it called the paradox of identification?

Accepted Answer

Identification in a simultaneous equations model (SEM) refers to the ability to uniquely determine the numerical values of the structural parameters (coefficients) from the observed data. In an SEM, variables are jointly determined, leading to endogeneity where endogenous regressors are correlated with the error term. Direct application of Ordinary Least Squares (OLS) to individual structural equations would yield biased and inconsistent estimates, making identification a critical first step.

T

Question 4

How do you express the multiple regression model in matrix form? Derive OLS estimator for the parameters of the model. Show that the OLS estimators are Best Linear Unbiased Estimators (BLUE).

Accepted Answer

The multiple regression model, which analyzes the relationship between a dependent variable and multiple independent variables, can be elegantly expressed in matrix form. This compact notation simplifies derivations and theoretical analysis.

In scalar form, the model for the i-th observation is given by Yᵢ = β₀ + β₁X₁ᵢ + β₂X₂ᵢ + ... + βₖXₖᵢ + εᵢ, where Yᵢ is the dependent variable, X₁ᵢ to Xₖᵢ are independent variables, β₀ to βₖ are parameters, and εᵢ is the error term. When extended to 'n' obs

Question 5

What is meant by multicollinearity? What are its consequences on estimates? What remedial measures do you suggest for the problem?

Accepted Answer

Multicollinearity, a concept extensively covered in MECE-101, refers to a situation in multiple regression analysis where two or more independent variables (regressors) in the model are highly, though not perfectly, linearly correlated with each other. While perfect multicollinearity (an exact linear relationship) is rare, high or imperfect multicollinearity is a common issue encountered in economic data, making it challenging for Ordinary Least Squares (OLS) to precisely estimate the unique eff

Question 6

Why is the OLS method inappropriate when a dataset is having heteroscedasticity problem? Explain the White's Test to detect heteroscedasticity in a data set.

Accepted Answer

The Ordinary Least Squares (OLS) method relies on several key assumptions for its estimators to possess desirable statistical properties, one of which is homoscedasticity. Homoscedasticity implies that the variance of the error terms (residuals) is constant across all observations, i.e., E(uᵢ²) = σ². When a dataset exhibits heteroscedasticity, this assumption is violated, meaning the variance of the error term is not constant but varies with the values of the independent variables.

Under hetero

Question 7

Write short notes on the following:

Accepted Answer

The Lagrange-Multiplier (LM) test and the Likelihood Ratio (LR) test are fundamental statistical inference tools in econometrics, particularly used for testing hypotheses concerning model parameters or specification. Both tests asymptotically follow a chi-squared distribution under the null hypothesis, with degrees of freedom equal to the number of restrictions being tested.

(a) The LM test is computationally efficient as it only requires estimating the restricted model. It evaluates whether r

MECE-101 Solved Assignment — January 2026 / July 2025

INTRODUCTORY ECONOMETRIC METHODS | IGNOU Master of Arts (Political Science) (MA)

MECE-101—January 2026 / July 2025

INTRODUCTORY ECONOMETRIC METHODS

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MECE-101 Assignment Questions — January 2026

Q1. In the case of a two-variable regression model show that TSS = ESS + RSS. Use appropriate diagram to explain your result. In this context, define the concept of R-squared and interpret it.

Q2. The relationship between Y and X is given by yi =x +ẞxi + u¡ where u¡ follows classical assumptions. Consider the following set of data and answer the questions. Y 11 12 13 14 15 X 18 16 19 22 20

Q3. Explain the concept of identification in a simultaneous equations model. Why is it called the paradox of identification?

Q4. How do you express the multiple regression model in matrix form? Derive OLS estimator for the parameters of the model. Show that the OLS estimators are Best Linear Unbiased Estimators (BLUE).

Q5. What is meant by multicollinearity? What are its consequences on estimates? What remedial measures do you suggest for the problem?

Q6. Why is the OLS method inappropriate when a dataset is having heteroscedasticity problem? Explain the White's Test to detect heteroscedasticity in a data set.

Q7. Write short notes on the following:

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