Question

which statement is true about a trend line?

a regression line and a trend line are opposite terms.
a regression line and trend line are equivalent terms.
a trend line represents only the smallest data points.
a trend line represents only the largest data points.

Explanation:

Analyze the definition of a trend line

A trend line (or line of best fit) is a straight line drawn through data points on a scatterplot to represent the general relationship and trend of the data.

Evaluate the relationship with a regression line

A regression line is the mathematically calculated line of best fit that minimizes the distances between the data points and the line. In statistics, "regression line" and "trend line" are used interchangeably to describe this line of best fit.

Evaluate the remaining options

The statements claiming a trend line represents only the smallest or largest data points are incorrect, as a trend line models the overall pattern of the entire dataset.

Answer:

• (A) A regression line and a trend line are opposite terms.
• (B) A regression line and trend line are equivalent terms. (Correct answer)
• (C) A trend line represents only the smallest data points.
• (D) A trend line represents only the largest data points.