Calculating one variable using another variable is done by

Explanation

## Correct Answer: B. Coefficient of Regression The **coefficient of regression** is the fundamental statistical tool used to predict or calculate the value of one variable based on another variable. It quantifies the relationship between a dependent variable (Y) and an independent variable (X) by establishing a linear equation: Y = a + bX, where 'b' is the regression coefficient. This coefficient represents the change in Y for every unit change in X. In clinical practice, regression is used to predict patient outcomes (e.g., estimating glomerular filtration rate from serum creatinine, predicting birth weight from maternal weight gain, or forecasting disease progression based on baseline parameters). The regression coefficient allows clinicians to make quantitative predictions about one variable when another is known, making it essential for prognostic modeling and clinical decision-making. Unlike correlation (which only measures strength of association), regression provides a predictive equation. This is why it is the correct answer for "calculating one variable using another." ## Why the other options are wrong **A. Coefficient of correlation** — Correlation measures the **strength and direction** of association between two variables (ranging from −1 to +1), but it does NOT allow prediction or calculation of one variable from another. It answers 'how related are they?' not 'what is the value of Y given X?' This is the most common trap—students confuse correlation with regression because both measure relationships. **C. Coefficient of variation** — The coefficient of variation (CV = SD/Mean × 100%) measures **relative variability or dispersion** within a single variable, expressed as a percentage. It is used to compare variability across different scales (e.g., comparing hemoglobin variation across age groups), not to predict one variable from another. It has no predictive function. **D. Coefficient of determination** — The coefficient of determination (R²) represents the **proportion of variance explained** by the regression model (0 to 1 scale). While it measures the goodness-of-fit of a regression model, it does NOT itself calculate or predict values. It tells you how well the regression model fits, not how to use it for prediction. ## High-Yield Facts - **Regression coefficient (b)** = change in dependent variable (Y) per unit change in independent variable (X); used for prediction via Y = a + bX - **Correlation coefficient (r)** measures association strength only (−1 to +1); does NOT predict values - **Coefficient of determination (R²)** = r² = proportion of variance in Y explained by X; ranges 0–1 - **Coefficient of variation (CV)** = (SD/Mean) × 100%; measures relative dispersion within ONE variable, not between two - In Indian clinical epidemiology, regression is used to predict outcomes like **maternal mortality risk** from socioeconomic factors or **TB cure rates** from treatment adherence ## Mnemonics **PREDICT vs RELATE** **Regression = PREDICT** (calculates Y from X); **Correlation = RELATE** (measures how linked they are). Use this when you see 'calculate,' 'predict,' or 'estimate'—always think regression. **R-squared (R²) vs r** **r** = correlation (−1 to +1, measures strength); **R²** = determination (0 to 1, explains variance). Remember: R² is derived FROM regression, not used FOR prediction itself. ## NBE Trap NBE often pairs "correlation" with "regression" in the same question set, exploiting the fact that both measure relationships. Students who conflate "measuring association" with "making predictions" will incorrectly choose correlation. The key discriminator is the verb: "calculating" or "predicting" = regression; "measuring strength" = correlation. ## Clinical Pearl In Indian public health programs (e.g., RNTCP, NRHM), regression models are used to predict TB treatment outcomes or estimate maternal mortality ratios from district-level socioeconomic data. A clinician using regression can say, "For every 10% increase in treatment adherence, cure rate increases by X%"—this predictive power is what makes regression indispensable in epidemiological surveillance and program evaluation. _Reference: Park's Textbook of Preventive and Social Medicine, Ch. 10 (Biostatistics); KD Tripathi Essentials of Medical Statistics, Ch. 5 (Correlation and Regression)_