Question

When do you use y' = y1/2?

A) Quadratic regression
B) Cubic regression
C) Square root regression
D) Inverse regression

Answer 1

C. Square root regression analysis.

The notation y' = y1/2 is used in Square root regression. This non-linear regression model fits data where the dependent variable is proportional to the square root of the independent variable. It differs from quadratic, cubic, and inverse regressions which fit parabolic, cubic, and inverse relationships respectively.

Step-by-step explanation:

The notation y' = y1/2 would be used in C. Square root regression analysis. A square root regression involves fitting a model to the data where the dependent variable (y) is proportional to the square root of the independent variable (x). This type of regression is used when the relationship between the dependent and independent variables is best described by a function involving the square root of the independent variable. Square root regression is one of several types of nonlinear regressions used for data that do not fit a linear pattern.

For other types of regressions:

• Quadratic regression would be for data that fits a parabolic trend (y = ax2 + bx + c).
• Cubic regression would be for data fitting a cubic equation (y = ax3 + bx2 + cx + d).
• Inverse regression would be for data fitting an inverse relationship (y = a/x or y = a + b/x).