Question

a y = 4x + 12
b y = 5x + 12
c y = 6x + 10
d y = 3x + 14

1. which r - value suggests a weak positive correlation?

a r = -0.23684
b r = 0.23684
c r = -0.97917
d r = 0.97917

1. the table shows the ages and weights of six kittens.

age (weeks)	2	4	6	8	10
weight (oz)	6	14	23	31	42

write the equation of the line that models the situation
do the data show a positive or a negative correlation?

Explanation:

20.

Step1: Recall correlation - coefficient rules

The correlation - coefficient \(r\) ranges from - 1 to 1. A positive \(r\) value indicates a positive correlation. Values close to 0 indicate a weak correlation, values close to 1 indicate a strong positive correlation, and values close to - 1 indicate a strong negative correlation.

Step2: Analyze each option

• Option A: \(r=-0.23684\) is a negative value, so it represents a negative correlation.
• Option B: \(r = 0.23684\) is a positive value and is close to 0, which suggests a weak positive correlation.
• Option C: \(r=-0.97917\) is close to - 1, indicating a strong negative correlation.
• Option D: \(r = 0.97917\) is close to 1, indicating a strong positive correlation.

Step1: Calculate the slope \(m\)

The formula for the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,6)\) and \((x_2,y_2)=(4,14)\). Then \(m=\frac{14 - 6}{4 - 2}=\frac{8}{2}=4\).
We can also use the point - slope form \(y - y_1=m(x - x_1)\) with the point \((x_1,y_1)=(2,6)\) and \(m = 4\).
\(y-6 = 4(x - 2)\)
\(y-6=4x-8\)
\(y=4x - 2\)

To check the correlation:
As the age (x - values: 2, 4, 6, 8, 10) increases, the weight (y - values: 6, 14, 23, 31, 42) also increases. So, the data show a positive correlation.

Answer:

B. \(r = 0.23684\)

21.