a y = 4x + 12\nb y = 5x + 12\nc y = 6x + 10\nd y = 3x + 14\n20. which r - value suggests a weak positive…
a y = 4x + 12\nb y = 5x + 12\nc y = 6x + 10\nd y = 3x + 14\n20. which r - value suggests a weak positive correlation?\na r = -0.23684\nb r = 0.23684\nc r = -0.97917\nd r = 0.97917\n21. the table shows the ages and weights of six kittens.\n| age (weeks) | 2 | 4 | 6 | 8 | 10 |\n| weight (oz) | 6 | 14 | 23 | 31 | 42 |\nwrite the equation of the line that models the situation\ndo the data show a positive or a negative correlation?
Answer
20.
Explanation:
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.
Answer:
B. (r = 0.23684)
21.
Explanation:
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:
Equation of the line: (y = 4x-2) Positive correlation