select the correct answer.

what is the relationship between the two variables represented in the table?

\begin{tabular}{|c|c|}
\hline
height of people (cm) & shoe size \\
\hline
170 & 8.5 \\
\hline
172 & 9 \\
\hline
174 & 9.5 \\
\hline
176 & 10 \\
\hline
178 & 11 \\
\hline
\end{tabular}

- positive linear association with no deviations
- exponential relationship
- negative linear association
- no relationship
- positive linear association with one deviation

Question

select the correct answer.

what is the relationship between the two variables represented in the table?

\begin{tabular}{|c|c|}
\hline
height of people (cm) & shoe size \\
\hline
170 & 8.5 \\
\hline
172 & 9 \\
\hline
174 & 9.5 \\
\hline
176 & 10 \\
\hline
178 & 11 \\
\hline
\end{tabular}

- positive linear association with no deviations
- exponential relationship
- negative linear association
- no relationship
- positive linear association with one deviation

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Association" ], "new_concepts": [], "current_concepts": [ "Linear Association", "Bivariate Data Analysis" ] } ## Analyze the rate of change between variables $$ \begin{aligned} &\Delta x_1 = 172 - 170 = 2, \quad \Delta y_1 = 9 - 8.5 = 0.5 \implies \frac{\Delta y_1}{\Delta x_1} = 0.25 \ &\Delta x_2 = 174 - 172 = 2, \quad \Delta y_2 = 9.5 - 9 = 0.5 \implies \frac{\Delta y_2}{\Delta x_2} = 0.25 \ &\Delta x_3 = 176 - 174 = 2, \quad \Delta y_3 = 10 - 9.5 = 0.5 \implies \frac{\Delta y_3}{\Delta x_3} = 0.25 \ &\Delta x_4 = 178 - 176 = 2, \quad \Delta y_4 = 11 - 10 = 1.0 \implies \frac{\Delta y_4}{\Delta x_4} = 0.50 \end{aligned} $$ ## Identify the deviation from the linear pattern $$ \begin{aligned} &\text{Constant rate of change for first 4 data points: } m = 0.25 \ &\text{Expected shoe size at } 178\text{ cm: } 10 + 0.5 = 10.5 \ &\text{Actual shoe size at } 178\text{ cm: } 11 \ &\text{Number of deviations from the linear trend: } 1 \end{aligned} $$ ## Determine the overall relationship $$ \begin{aligned} &\text{Since } y \text{ generally increases as } x \text{ increases: Positive association} \ &\text{Since there is exactly one point violating the constant slope: Positive linear association with one deviation} \end{aligned} $$

positive linear association with no deviations

exponential relationship

negative linear association

no relationship

positive linear association with one deviation

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Linear Association" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the rate of change between variables

Identify the deviation from the linear pattern

Determine the overall relationship

Answer: