Statistics

Which graph shows a strong positive correlation?

Step-by-step solution with explanation

Final Answer

The correct graph shows a scatter plot where points are tightly clustered in an upward trend from lower-left to upper-right, representing a correlation coefficient r close to +1 (strong positive correlation).

Step-by-step solution

1

Define what correlation means

Correlation describes how two variables move together. The correlation coefficient r ranges from -1 to +1.
2

Identify a positive correlation

A positive correlation means as the x-values increase, the y-values also increase. The data points trend upward from left to right.
3

Identify a STRONG positive correlation

Strong means the points are clustered tightly around an imaginary line going up to the right. The closer r is to +1, the stronger and tighter the pattern.
4

Recognize what the graph looks like

Look for a scatter plot where dots go from lower-left to upper-right in a narrow, tight cluster. Loose or scattered points mean weak correlation. A downward trend means negative correlation.

Understanding this problem

Learning Insight

Correlation measures both direction (positive or negative) and strength (strong or weak). A strong positive correlation means knowing x gives you a very good prediction of y — the two variables are closely linked in an upward pattern. This does NOT mean one causes the other, just that they move together.

Quick Tip

Picture a straight line drawn through the dots. If the dots hug that line tightly AND the line goes uphill left-to-right, it is a strong positive correlation.

Common Mistake

Students often confuse steep slope with strong correlation. A line can be very steep but the points can still be loosely scattered — slope and strength of correlation are different things.