**Question:** The regression between height and age follows y = a + bx. The curve is -

A. linear
B. exponential
C. logarithmic
D. polynomial

**Correct Answer:** A. linear

**Core Concept:** Linear regression is a method used to analyze the relationship between two variables, in this case, height (y) and age (x). The equation y = a + bx represents this relationship, where 'a' is the y-intercept and 'b' is the slope of the line. The curve representing this relationship is a straight line.

**Why the Correct Answer is Right:** The correct answer is linear because the equation demonstrates a simple correlation between height and age, where both variables affect the outcome (height) directly. A linear relationship ensures that for every unit change in age, there is a corresponding unit change in height.

**Why Each Wrong Option is Incorrect:**

A. Exponential Regression (Option B): An exponential regression would imply a relationship where the change in height is not directly proportional to the change in age. In this case, the relationship is linear, not exponential.

C. Logarithmic Regression (Option C): Logarithmic regression would involve a relationship where the height change is related to the natural logarithm of age. This is different from the linear regression presented in the question.

D. Polynomial Regression (Option D): Polynomial regression involves higher-order relationships between variables, where the change in height is related to the square, cube, or higher powers of age. The question demonstrates a simple linear relationship and does not involve polynomial regression.

**Clinical Pearl:** Understanding linear regression is essential for medical professionals, as it helps in interpreting data correlation in various clinical scenarios, including analyzing growth patterns, predicting disease progression, or evaluating treatment effectiveness.