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 

1.61.6 

​cm, using the regression equation. Can the prediction be​ correct? If​ not, what is​ wrong? Use a significance level of 

0.050.05.

Overhead Width​ (cm)

7.17.1

7.57.5

9.89.8

9.39.3

8.88.8

8.48.4
 
Weight​ (kg)

112112

158158

245245

198198

200200

191191

Question content area bottom

Part 1

The regression equation is 

ModifyingAbove y with caretyequals=nothing plus left parenthesis nothing right parenthesis xenter your response here+enter your response herex.

​(Round the​ y-intercept to 

the nearest integerthe nearest integer 

as needed. Round the slope to one decimal place as​ needed.)

The regression equation is:

\[
\hat{y} = -165 + 41.1x
\]

Where:
- \(\hat{y}\) is the predicted weight,
- \(x\) is the overhead width in cm.

Using this equation, the predicted weight of a seal with an overhead width of 1.6 cm is approximately:

\[
\hat{y} = -165 + 41.1(1.6) = -98.83 \, \text{kg}
\]

This prediction is clearly unrealistic because weight cannot be negative. The issue arises because the overhead width of 1.6 cm is far outside the range of the data provided (which ranges from 7.1 to 9.8 cm). Therefore, the prediction is invalid since it's an extrapolation beyond the meaningful range of the data.

Would you like more details, or do you have any questions? Here are five related questions you might find interesting:
1. How does extrapolation affect the accuracy of predictions?
2. Can we improve this model by adding more data points within a realistic range?
3. What does the \(r\)-value indicate about the strength of this regression model?
4. What assumptions underlie the use of linear regression for this data?
5. How can we verify if linear regression is the best fit for this type of data?

**Tip:** Always check that the prediction inputs fall within the range of the original data to avoid inaccurate extrapolations.

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 1.6 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): 7.1, 7.5, 9.8, 9.3, 8.8, 8.4. Weight (kg): 112, 158, 245, 198, 200, 191.

Learn how to calculate the regression equation for predicting seal weights based on overhead width measurements. This example uses a significance level of 0.05 and includes data points ranging from 7.1 to 9.8 cm for overhead widths and 112 to 245 kg for weights. Suitable for students in Grades 10-12.

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