To evaluate Kardal's prediction about the shoe size for a man who is 72 inches tall based on the trend line from the graph, let's analyze each statement.
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The prediction is not reasonable.
- This statement may or may not be true depending on the accuracy of the trend line and existing data. Without additional context or data, we cannot definitively conclude that it is unreasonable.
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The prediction is an interpolation.
- This statement is not true. Interpolation refers to predicting a value within the range of existing data points. Since 72 inches is beyond the maximum known height from the given points (70 inches), this prediction would be considered extrapolation, not interpolation.
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No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.
- This statement is true. Even though there is no data point for 72 inches, the trend line allows for a prediction to be made.
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A prediction cannot be made without the linear regression equation.
- This statement is not entirely true. While having the linear regression equation could provide a more accurate prediction, predictions can still be made using the trend line graphically, as Kardal did.
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A 72-inch tall man will wear a size 11.5 shoe.
- This statement does not follow directly from the trend line as stated. Kardal predicted a size 10.5, so this assertion contradicts his prediction.
In summary, the correct conclusions based on the scenario are:
- No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.
The other statements may not be accurate or relevant to the prediction scenario described.
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