Question

which table shows no correlation?

x | 3 | 5 | 6 | 8 | 10 | 14 | 15
y | -1 | -2 | -3 | -2 | -5 | -4 | -8

x | 3 | 5 | 6 | 8 | 10 | 14 | 15
y | -6 | -7 | -4 | -2 | 0 | -1 | 3

x | 3 | 5 | 6 | 8 | 10 | 14 | 15
y | -2 | -4 | 6 | 8 | 12 | 10 | -16

x | 3 | 5 | 6 | 8 | 10 | 14 | 15
y | -3 | -5 | -9 | -11 | -13 | -15 | -17

Explanation:

Step1: Understand Correlation

Correlation means a relationship between \( x \) and \( y \) values. Positive correlation: as \( x \) increases, \( y \) generally increases. Negative correlation: as \( x \) increases, \( y \) generally decreases. No correlation: \( y \) values have no clear pattern with \( x \) increases.

Step2: Analyze First Table

\( x \): 3, 5, 6, 8, 10, 14, 15 (increasing)
\( y \): -1, -2, -3, -2, -5, -4, -8. There's a general negative trend ( \( y \) decreases as \( x \) increases, mostly). So negative correlation.

Step3: Analyze Second Table

\( x \): 3, 5, 6, 8, 10, 14, 15 (increasing)
\( y \): -6, -7, -4, -2, 0, -1, 3. As \( x \) increases, \( y \) generally increases (from -6 to 3). Positive correlation.

Step4: Analyze Third Table

\( x \): 3, 5, 6, 8, 10, 14, 15 (increasing)
\( y \): -2, -4, 6, 8, 12, 10, -16. \( y \) values: -2, -4 (decrease), then 6,8,12 (increase), then 10, -16 (decrease). No clear upward/downward trend. So no correlation.

Step5: Analyze Fourth Table

\( x \): 3, 5, 6, 8, 10, 14, 15 (increasing)
\( y \): -3, -5, -9, -11, -13, -15, -17. As \( x \) increases, \( y \) consistently decreases. Strong negative correlation.

Answer:

The table with \( x \) values 3, 5, 6, 8, 10, 14, 15 and \( y \) values -2, -4, 6, 8, 12, 10, -16 (the third table) shows no correlation.