Question

which of the following scatter diagrams suggests the following conclusions?
(a) strongest positive linear correlation between the x and y variables
graph a
graph b
graph c
graph d
(b) strongest negative linear correlation between the x and y variables
graph a
graph b
graph c
graph d

Explanation:

Step1: Understand positive and negative correlation

Positive correlation: as \(x\) increases, \(y\) increases. Negative correlation: as \(x\) increases, \(y\) decreases.

Step2: Analyze strength of correlation

The closer the points are to a straight - line, the stronger the correlation.

• For positive correlation:
• In graph \(a\), points are scattered. In graph \(b\), points are close to a straight - line with positive slope.
• For negative correlation:
• In graph \(c\), points are close to a straight - line with negative slope. In graph \(d\), points are scattered.

Answer:

(a) graph b
(b) graph c