Question

a scatterplot has a positive, linear correlation. which statement is true about the relationship between the \\(x\\)- and \\(y\\)-values?

as the \\(x\\)-values increase, the \\(y\\)-values tend to increase.
as the \\(x\\)-values increase, the \\(y\\)-values tend to decrease.
as the \\(x\\)-values decrease, the \\(y\\)-values tend to increase.
as the \\(x\\)-values decrease, the \\(y\\)-values tend to vary randomly.

Explanation:

Define positive correlation

A positive correlation between two variables means that as one variable increases, the other variable also tends to increase.

Analyze the given options

• Option 1: "As the \(x\)-values increase, the \(y\)-values tend to increase." This matches the definition of a positive correlation.
• Option 2: "As the \(x\)-values increase, the \(y\)-values tend to decrease." This describes a negative correlation.
• Option 3: "As the \(x\)-values decrease, the \(y\)-values tend to increase." This also describes a negative correlation.
• Option 4: "As the \(x\)-values decrease, the \(y\)-values tend to vary randomly." This describes no correlation.

Answer:

• (A) As the \(x\)-values increase, the \(y\)-values tend to increase. (Correct answer)
• (B) As the \(x\)-values increase, the \(y\)-values tend to decrease.
• (C) As the \(x\)-values decrease, the \(y\)-values tend to increase.
• (D) As the \(x\)-values decrease, the \(y\)-values tend to vary randomly.