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 51 inches. is the result close to the actual weight of 442 pounds? use a significance level of 0.05.
chest size (inches) | 45 50 43 43 52 52
weight (pounds) | 352 374 275 314 440 367
click the icon to view the critical values of the pearson correlation coefficient r.
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what is the regression equation?
ŷ = -172.6 + 11.1 x (round to one decimal place as needed.)
what is the best predicted weight of a bear with a chest size of 51 inches?
the best predicted weight for a bear with a chest size of 51 inches is pounds.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = -172.6 + 11.1x$, where $x$ is the chest size (in inches) and $\hat{y}$ is the predicted weight (in pounds).

Step2: Substitute x = 51 into the regression equation

We substitute $x = 51$ into the equation $\hat{y} = -172.6 + 11.1x$.
So, $\hat{y} = -172.6 + 11.1\times51$.

First, calculate $11.1\times51$:
$11.1\times51 = 11.1\times(50 + 1) = 11.1\times50 + 11.1\times1 = 555 + 11.1 = 566.1$.

Then, calculate $\hat{y} = -172.6 + 566.1$.
$\hat{y} = 566.1 - 172.6 = 393.5$.

Answer:

393.5