Question

evaluating a prediction
kardal used the trend line to predict that a man 72 inches tall would wear about a size 10.5 shoe. what can be concluded about this prediction? check all that apply.
the prediction is not reasonable.
the prediction is an interpolation.
no data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.
a prediction cannot be made without the linear regression equation.
a 72 - inch tall man will wear a size 11.5 shoe.

Explanation:

• Interpolation vs. Extrapolation: Since \(72\) inches is within the range of \(x\) - values (height values) in the scatter - plot (assuming the \(x\) - axis range includes values around \(72\)), it is not an extrapolation. But the statement "The prediction is an interpolation" is incorrect because interpolation is for values within the data - point range of the independent variable where data points exist. Here, there is no data point at \(x = 72\).
• Prediction without Data Point: Just because there is no data point at \(x=72\) (height = 72 inches), we can still use the trend line (which is based on the linear relationship of the existing data points) to predict the shoe size.
• Prediction and Linear Regression Equation: While the linear regression equation is a formal way to make predictions, we can also make a prediction using the trend line (a visual representation of the linear relationship) drawn on the scatter - plot.
• Accuracy of Prediction: We cannot say the prediction is not reasonable just from the given information. Also, the trend line in the plot does not suggest a size \(11.5\) for \(x = 72\).

Answer:

No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted.