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 relationship between a trend line and a regression line

A trend line is a line drawn on a scatterplot to show the general direction and relationship of the data points. A regression line (specifically the least-squares regression line) is a mathematically calculated trend line that minimizes the distance between itself and all the data points. Therefore, "regression line" and "trend line" are equivalent terms in this context.

Evaluate the remaining options

• Opposite terms: Incorrect, as they describe the same general concept of modeling data trends.
• Represents only the smallest/largest data points: Incorrect, as a trend line represents the overall pattern of the entire dataset, not just extreme values.

Answer:

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