Question

determine the strength and direction of the correlation between the variables in the context of the scenario.

• there is a strong, negative correlation between the variables.
• there is a strong, positive correlation between the age and weight of puppies.
• there is a weak, positive correlation between the age and weight of puppies.
• there is a weak, negative relationship between the age and weight of puppies.

Explanation:

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<reasoning>

Analyze the direction of the correlation

Using the Scatter Plots knowledge point
\[

$$\begin{aligned} &\text{As } x \text{ (Age in days) increases from } 1 \text{ to } 9,\\ &\text{the values of } y \text{ (Weight) generally increase from } 2.5 \text{ to } 5.0 \text{ and } 6.0.\\ &\text{Since } y \text{ tends to increase as } x \text{ increases, the correlation is positive.} \end{aligned}$$

\]

Determine the strength of the correlation

Using the Correlation Strength knowledge point
\[

$$\begin{aligned} &\text{Let } \bar{x} = 3.67, \quad \bar{y} = 4.28\\ &s_x \approx 2.69, \quad s_y \approx 1.09\\ &r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n-1)s_x s_y} \approx 0.76\\ &\text{Since } 0.7 \le r < 0.9, \text{ the correlation is strong.} \end{aligned}$$

\]

Evaluate the options in context

Using the Correlation Strength knowledge point
\[

$$\begin{aligned} &\text{Variables: } x = \text{Age (days)}, \quad y = \text{Weight (puppies)}\\ &\text{Direction: Positive}\\ &\text{Strength: Strong}\\ &\text{Conclusion: There is a strong, positive correlation between the age and weight of puppies.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>There is a strong, negative correlation between the variables.</mcq-option>
<mcq-correct>There is a strong, positive correlation between the age and weight of puppies.</mcq-correct>
<mcq-option>There is a weak, positive correlation between the age and weight of puppies.</mcq-option>
<mcq-option>There is a weak, negative relationship between the age and weight of puppies.</mcq-option>
</answer>

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"Correlation Strength"
]
}
</post_analysis>

Answer:

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<reasoning>

Analyze the direction of the correlation

Using the Scatter Plots knowledge point
\[

$$\begin{aligned} &\text{As } x \text{ (Age in days) increases from } 1 \text{ to } 9,\\ &\text{the values of } y \text{ (Weight) generally increase from } 2.5 \text{ to } 5.0 \text{ and } 6.0.\\ &\text{Since } y \text{ tends to increase as } x \text{ increases, the correlation is positive.} \end{aligned}$$

\]

Determine the strength of the correlation

Using the Correlation Strength knowledge point
\[

$$\begin{aligned} &\text{Let } \bar{x} = 3.67, \quad \bar{y} = 4.28\\ &s_x \approx 2.69, \quad s_y \approx 1.09\\ &r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n-1)s_x s_y} \approx 0.76\\ &\text{Since } 0.7 \le r < 0.9, \text{ the correlation is strong.} \end{aligned}$$

\]

Evaluate the options in context

Using the Correlation Strength knowledge point
\[

$$\begin{aligned} &\text{Variables: } x = \text{Age (days)}, \quad y = \text{Weight (puppies)}\\ &\text{Direction: Positive}\\ &\text{Strength: Strong}\\ &\text{Conclusion: There is a strong, positive correlation between the age and weight of puppies.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>There is a strong, negative correlation between the variables.</mcq-option>
<mcq-correct>There is a strong, positive correlation between the age and weight of puppies.</mcq-correct>
<mcq-option>There is a weak, positive correlation between the age and weight of puppies.</mcq-option>
<mcq-option>There is a weak, negative relationship between the age and weight of puppies.</mcq-option>
</answer>

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