In Simple Regression Analysis, If the Correlation Coefficient Is a Positive

question 68

Multiple Choice

In simple regression analysis, if the correlation coefficient is a positive value, then

• A) the y-intercept must also be a positive value.
• B) the coefficient of determination can be either positive or negative, depending on the value of the slope.
• C) the least squares regression equation could have either a positive or a negative slope.
• D) the slope of the regression line must also be positive.
• E) the standard error of estimate can have either a positive or a negative value.

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Definitions:

Method of Substitution

A technique used to solve systems of equations where one equation is solved for one variable, which is then substituted into other equations.

Hyperbola

A type of smooth curve lying in a plane, defined by its geometric properties or by equations that are not necessarily of the second degree. Specifically, it refers to a conic section that is not a circle, ellipse, or parabola.

Center and Vertices

Terms related to conic sections; the center is a central point of the shape, while vertices are points where the curve intersects its principal axis.

Graph Equations

The process of plotting the solutions to an equation on a graph, typically within a coordinate system.