A Least-Squares Regression Line Is Not Just Any Line Drawn

question 18

Multiple Choice

A least-squares regression line is not just any line drawn through the points of a scatterplot. What is special about a least-squares regression line?

• A) It passes through all the points.
• B) It minimizes the squared values of the data.
• C) It has slope equal to the correlation between the two variables.
• D) It describes how a response variable y changes as an explanatory variable x takes different values.
• E) It minimizes the sum of the squared vertical distances of the data points from the line.

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Definitions:

Bivariate Data

Data involving two variables that can be analyzed for relationships and patterns between them.

Multivariate Data

Data involving two or more variables or attributes, allowing for analysis of relationships and patterns among these variables.

Population

The entire group of individuals or instances about whom we hope to learn in a statistical analysis.

Sample

A subset of a larger population selected for measurement, observation, or questioning to make inferences about the whole.