Question

the data show the chest size and weight of several bears. find the regression equation, let chest size be the independent (x) variable. then find the best predicted weight of a bear with chest size of 63 inches. is the result close to the actual weight of 462 pounds? use a significance level of 0.05.
chest size (inches) | 58 | 50 | 65 | 59 | 59 | 48
weight (pounds) | 414 | 312 | 499 | 450 | 456 | 260
click the icon to view the critical values of the pearson correlation coefficient r.
ŷ = -411.7 + 14.4x (round to one decimal place as needed.)
what is the best predicted weight of a bear with a chest size of 63 inches?
the best predicted weight for a bear with a chest size of 63 inches is 495.5 pounds. (round to one decimal place as needed.)
is the result close to the actual weight of 462 pounds?
a. this result is exactly the same as the actual weight of the bear.
b. this result is close to the actual weight of the bear.
c. this result is very close to the actual weight of the bear.
d. this result is not very close to the actual weight of the bear.

Explanation:

Step1: Identify the predicted and actual weights

Predicted weight ($\hat{y}$) for chest size 63 inches is 495.5 pounds. Actual weight is 462 pounds.

Step2: Calculate the difference

Difference = |495.5 - 462| = 33.5 pounds. A difference of 33.5 pounds (considering the scale of weights) is not very close. So the result is not very close to the actual weight.

Answer:

D. This result is not very close to the actual weight of the bear.