the table below shows the lengths and weights of six dolphins at an aquarium. use the data from pax and…
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?\n\n| name | length (ft) | weight (lb) |\n| ---- | ---- | ---- |\n| snowflake | 8.2 | 549 |\n| shadow | 7.4 | 501 |\n| corky | 8.4 | 557 |\n| pax | 7.6 | 519 |\n| jojo | 5.8 | 460 |\n| blaze | 6.8 | 488 |\n\no blaze\no jojo\no corky\no shadow
Answer
Explanation:
Step1: Find the slope of the linear model
The formula for the slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Pax ($x_1 = 7.6,y_1=519$) and Snowflake ($x_2 = 8.2,y_2 = 549$), we have $m=\frac{549 - 519}{8.2-7.6}=\frac{30}{0.6}=50$.
Step2: Find the y - intercept of the linear model
Use the point - slope form $y - y_1=m(x - x_1)$ and rewrite it in slope - intercept form $y=mx + b$. Using the point $(x_1,y_1)=(7.6,519)$ and $m = 50$, we get $y-519=50(x - 7.6)$. Then $y-519=50x-380$, and $y = 50x+139$.
Step3: Calculate the predicted weights for each dolphin
For Shadow: $x = 7.4$, $y_{predicted}=50\times7.4 + 139=370+139 = 509$. The difference is $|501 - 509|=8$. For Corky: $x = 8.4$, $y_{predicted}=50\times8.4+139=420 + 139=559$. The difference is $|557 - 559|=2$. For JoJo: $x = 5.8$, $y_{predicted}=50\times5.8+139=290+139 = 429$. The difference is $|460 - 429|=31$. For Blaze: $x = 6.8$, $y_{predicted}=50\times6.8+139=340+139 = 479$. The difference is $|488 - 479|=9$.
Answer:
JoJo