प्रतिदर्श आकार (Sample size) बढ़ाने पर प्रतिचयन त्रुटि (Sampling... | Agrigyan

Analysis of the principle of least squares:

• Incorrect: Maximizing squared errors would fit the worst possible line.
• Correct: The method of least squares estimates regression parameters by finding line coefficients that minimize the sum of the squared vertical deviations (residuals) between the observed values and fitted values: $\sum e_i^2 = \sum (y_i - \hat{y}_i)^2 = \text{minimum}$.
• Incorrect: Sum of squared deviations cannot be zero unless all points lie perfectly in a straight line with zero error.
• Incorrect: Sums of squares are non-negative and can never be negative.

Analysis of random variable types:

• Incorrect: 'Uncertain random variable' is not a formal mathematical classification.
• Incorrect: 'Irregular random variable' is not a standard statistical term.
• Incorrect: A discrete random variable can take only distinct, countable isolated values (such as integers 0, 1, 2, ...).
• Correct: A continuous random variable is defined as a variable that can assume an uncountable infinity of values, taking any real value within a given continuum or interval $[a, b]$ (such as height, weight, temperature, or time).

Analysis of census periodicity:

• Correct: National census organizations (such as the Office of the Registrar General & Census Commissioner in India, and the US Census Bureau) conduct complete comprehensive population censuses decennially, i.e., once every 10 years.
• Incorrect: Agricultural censuses and livestock censuses in India are conducted at 5-year intervals, but comprehensive population censuses are conducted every 10 years.
• Incorrect: 2-year cycles are not used for complete censuses.
• Incorrect: Annual counts are sample estimates (e.g. American Community Survey or SRS), not full census counts.