Answer:
The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
Step-by-step explanation:
Name Length (ft) Weight (lb)
Snowflake 8.2 549
Shadow 7.4 501
Corky 8.4 557
Pax 7.6 519
JoJo 5.8 460
Blaze 6.8 488
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 dolphin's weight differs most from the value predicted by this model?
Let's elaborate the model this way:
Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft
Snowflake's weight - Pax's weight = 549 - 519 = 30 lb
Ratio = 30/0.6 = 50 lb/ft
This means that for every foot of length, the dolphin has a variable weight of 50 lb. However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:
Snowflake = 50 * 8.2 = 410
Pax = 50 * 7.6 = 380
What is the common difference in both cases?
Snowflake = Actual weight - Ratio * Length = 549 - 410 = 139
Pax = Actual weight - Ratio * Length = 519 - 380 = 139
The common difference is 139. Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:
y = 139 + 50x
Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:
Blaze y = 139 + 50 * 6.8 = 479 ⇒ difference of 9 lb (488 - 479)
JoJo y = 139 + 50 * 5.8 = 429 ⇒ difference of 31 lb (460 - 429)
Corky y = 139 + 50 * 8.4 = 559 ⇒ difference of 2 lb (559 - 557)
Shadow y = 139 + 50 * 7.4 = 509 ⇒ difference of 8 lb (509 - 501)
The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
