the table below shows the lengths and weights of six dolphins at an aquarium. use the data from pax and snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). which dolphins weight differs most from the value predicted by this model?

\begin{tabular}{|c|c|c|}
\hline
name & length (ft) & weight (lb) \\
\hline
snowflake & 8.2 & 549 \\
\hline
shadow & 7.4 & 501 \\
\hline
corky & 8.4 & 557 \\
\hline
pax & 7.6 & 519 \\
\hline
jojo & 5.8 & 460 \\
\hline
blaze & 6.8 & 488 \\
\hline
\end{tabular}

- blaze
- jojo
- corky
- shadow

Question

the table below shows the lengths and weights of six dolphins at an aquarium. use the data from pax and snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). which dolphins weight differs most from the value predicted by this model?

\begin{tabular}{|c|c|c|}
\hline
name & length (ft) & weight (lb) \\
\hline
snowflake & 8.2 & 549 \\
\hline
shadow & 7.4 & 501 \\
\hline
corky & 8.4 & 557 \\
\hline
pax & 7.6 & 519 \\
\hline
jojo & 5.8 & 460 \\
\hline
blaze & 6.8 & 488 \\
\hline
\end{tabular}

- blaze
- jojo
- corky
- shadow

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Modeling", "Linear Functions" ], "new_concepts": [ "Residual Analysis" ], "current_concepts": [ "Linear Modeling", "Linear Functions", "Residual Analysis" ] } ## Create the linear model using Pax and Snowflake $$ \begin{aligned} &\text{Pax: } (x_1, y_1) = (7.6, 519) \ &\text{Snowflake: } (x_2, y_2) = (8.2, 549) \ &m = \frac{549 - 519}{8.2 - 7.6} = \frac{30}{0.6} = 50 \ &y - 519 = 50(x - 7.6) \ &y = 50x - 380 + 519 \ &y = 50x + 139 \end{aligned} $$ ## Calculate predicted weights and absolute residuals $$ \begin{aligned} &\text{Shadow } (x = 7.4, y = 501): \hat{y} = 50(7.4) + 139 = 509 \implies |y - \hat{y}| = |501 - 509| = 8 \ &\text{Corky } (x = 8.4, y = 557): \hat{y} = 50(8.4) + 139 = 559 \implies |y - \hat{y}| = |557 - 559| = 2 \ &\text{JoJo } (x = 5.8, y = 460): \hat{y} = 50(5.8) + 139 = 429 \implies |y - \hat{y}| = |460 - 429| = 31 \ &\text{Blaze } (x = 6.8, y = 488): \hat{y} = 50(6.8) + 139 = 479 \implies |y - \hat{y}| = |488 - 479| = 9 \end{aligned} $$ ## Identify the dolphin with the largest difference $$ \begin{aligned} &\max(8, 2, 31, 9) = 31 \quad (\text{JoJo}) \end{aligned} $$

Blaze

JoJo

Corky

Shadow

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Create the linear model using Pax and Snowflake

Calculate predicted weights and absolute residuals

Identify the dolphin with the largest difference

Answer: