Question

listed below are the overhead widths (cm) of seals measured from photographs and weights (kg) of the seals. find the regression equation, letting the overhead width be the predictor (x) variable. find the best predicted weight of a seal if the overhead width measured from a photograph is 2.3 cm, using the regression equation. can the prediction be correct? if not, what is wrong? use a significance level of 0.05. overhead width (cm) 7.2 7.4 9.8 9.3 8.7 8.4 weight (kg) 121 159 252 205 203 196 the regression equation is ŷ = -161 + (41.4)x. (round the y-intercept to the nearest integer as needed. round the slope to one decimal place as needed.) the best predicted weight for an overhead width of 2.3 cm, based on the regression equation, is □ kg. (round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = -161 + 41.4x$, where $x$ is the overhead width (in cm) and $\hat{y}$ is the predicted weight (in kg).

Step2: Substitute the given x - value

We are given that the overhead width $x = 2.3$ cm. Substitute $x = 2.3$ into the regression equation:
$\hat{y}=- 161+41.4\times2.3$

Step3: Calculate the value of $\hat{y}$

First, calculate $41.4\times2.3$:
$41.4\times2.3 = 41.4\times(2 + 0.3)=41.4\times2+41.4\times0.3 = 82.8+12.42=95.22$
Then, calculate $\hat{y}=-161 + 95.22=- 65.78\approx - 65.8$ (rounded to one decimal place)

Answer:

-65.8