Question

the data show the chest size and weight of several bears. find the regression equation, letting chest size be the independent (x) variable. then find the best predicted weight of a bear with a chest size of 40 inches. is the result close to the actual weight of 382 pounds? use a significance level of 0.05.
chest size (inches) | 41 | 54 | 44 | 55 | 39 | 51
weight (pounds) | 328 | 528 | 418 | 580 | 296 | 503
click the icon to view the critical values of the pearson correlation coefficient r.
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what is the regression equation?
ŷ = -330.4 + 16.4 x (round to one decimal place as needed.)
what is the best predicted weight of a bear with a chest size of 40 inches?
the best predicted weight for a bear with a chest size of 40 inches is pounds.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = -330.4 + 16.4x$, where $x$ is the chest size (inches) and $\hat{y}$ is the predicted weight (pounds).

Step2: Substitute x = 40 into the regression equation

We need to find the predicted weight when $x = 40$. Substitute $x = 40$ into the equation:

$$ \hat{y} = -330.4 + 16.4 \times 40 $$

Step3: Calculate the value

First, calculate $16.4 \times 40 = 656$. Then, subtract 330.4 from 656:

$$ \hat{y} = -330.4 + 656 = 325.6 $$

Answer:

325.6